REVIEW 3 major objections 5 minor 125 references
Universal limitations on implementing resourceful unitary evolutions
T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read The paper proves a universal limitation: a unitary that changes a quantum resource cannot be perfectly realized with free unitaries and finite ancilla, and it quantifies the accuracy–ancilla trade-off.
desk verdict A clean general no-go for implementing resourceful unitaries with finite ancillas, with a localized but real overreach in the qubit-magic application that a referee should catch. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The machinery has three parts. The resource generating power $G_U:=\max_\rho\{R(U\rho U^\dagger)-R(\rho)\}$ and resource losing power $L_U:=-\min_\rho\{R(U\rho U^\dagger)-R(\rho)\}$ measure how much resource the target unitary can create or destroy. The no-correlation lemma (reproduced from earlier work as Lemma 7) says that an approximate implementation forces the final ancilla state to be nearly independent of the input, with a quantitative bound on how close the environment states for two distinguished inputs must be. The proof combines this lemma with the three properties of $R$—invariance under free unitaries, Lipschitz-type continuity, and additivity on product states—to bound $G_{U_S}+L_{U_S}$ by the error and ancilla dimension. The relaxed theorem uses the pure-state version of additivity plus the fact that a pure ancilla state gives a pure intermediate reference state.
What would settle it
Find one counterexample: a resource measure $R$ satisfying Properties 1–3, a finite-dimensional ancilla, and a free unitary $V$ such that $\mathrm{Tr}_E[V(\rho_S\otimes\rho_E)V^\dagger]$ exactly equals $U_S\rho_S U_S^\dagger$ for all $\rho_S$ while $G_{U_S}+L_{U_S}>0$; the theorem says none exists, so an explicit construction or numerical search that finds one would settle the matter.
Extended reading notes
Core claim
The central claim is Theorem 1: for any resource measure $R$ satisfying invariance under free unitaries, continuity, and additivity for product states, and for any implementation $I=(H_E,V_{SE},\rho_E)$ of a unitary $U_S$ using a free unitary $V_{SE}$ and an ancilla of dimension $d_E$, one has $G_{U_S}+L_{U_S}\le \alpha_L(\delta^I_{U_S},d_E)+\beta_L(\delta^I_{U_S})$, where $G_{U_S}$ and $L_{U_S}$ are the maximum resource increase and decrease $U_S$ can induce, $\delta^I_{U_S}$ is the worst-case gate error, and $\alpha_L,\beta_L$ vanish as the error and the inverse ancilla dimension go to zero. The immediate corollary is that a unitary with $G_{U_S}+L_{U_S}>0$ cannot be perfectly implemented with a finite-dimensional ancilla. A second theorem relaxes additivity to pure product states and yields the same conclusion for implementations with a pure ancilla state. The paper then verifies the hypotheses for specific measures—energy expectation, Wigner–Yanase skew information, athermality, relative entropy of coherence, squashed entanglement, relative entropy of entanglement, stabilizer extent, and mana—so the no-go conclusion covers those settings.
Load-bearing premise
The entire argument hangs on the no-correlation lemma taken from earlier work without proof—that any approximate implementation of a unitary leaves the environment nearly uncorrelated with the system input; if that lemma fails, the trade-off and the no-go theorem collapse.
Editorial extensions
If this is right
- Corollary 2: for any resource theory with a measure satisfying Properties 1–3, no unitary with nonzero resource-generating or resource-losing power can be perfectly implemented with a finite-dimensional ancilla and free unitaries alone.
- The trade-off is quantitative: as the allowed error $\delta$ goes to zero, the ancilla dimension must grow without bound; Theorem 1 gives the explicit functional dependence through $\alpha_L$ and $\beta_L$.
- The results reproduce the known energy-conservation no-go theorem as a special case, using the energy expectation value as the resource measure.
- In the theory of coherence, any coherence-generating unitary is impossible to implement exactly with a finite coherent ancilla; in entanglement theory, any entangling gate is impossible with local unitaries and finite shared entanglement (without classical communication).
- For fault-tolerant computation, implementing a non-Clifford gate with Clifford unitaries and magic states requires the number of ancilla qubits to grow at least as $\Omega(\log((G^p_{U_{NC}}+L^p_{U_{NC}})/\sqrt{\epsilon}))$ for accuracy $\epsilon$.
Reading between the lines
- A direct but unstated corollary is that adaptive protocols involving measurement and feedforward can evade the dimensional bound, because the theorem applies only to unitary circuits without intermediate measurements; gate teleportation is the standard example.
- The same no-correlation logic could likely be applied to channels rather than unitaries, yielding analogous trade-offs for resource-changing quantum channels; this is a natural testable extension the paper does not explore.
- The lower bounds are not shown to be tight; constructing explicit approximate implementations that saturate them would clarify whether the required ancilla dimension is really as large as the theorem suggests.
- Because the no-go holds for any additive continuous measure, it suggests that exact resource-changing operations require either an infinite-dimensional reference frame or some non-unitary ingredient, which may have consequences for superselection rules and thermodynamic batteries.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proves a general trade-off relation for implementing a target unitary U_S using only free unitaries acting on the system together with an ancilla. For any resource measure R satisfying invariance under free unitaries, a continuity condition, and additivity for product states, Theorem 1 bounds the resource generating/losing power G_U_S + L_U_S in terms of the implementation error and the ancilla dimension, with the bound vanishing as the error and the inverse ancilla dimension tend to zero. Corollary 2 derives a no-go result: no resource-changing unitary can be perfectly implemented with a finite-dimensional ancilla. Theorem 4 relaxes additivity to pure product states and gives an analogous bound. The paper applies the framework to energy, asymmetry, coherence, entanglement, and magic. For qubit magic, it uses the log stabilizer extent as the resource measure and invokes multiplicativity results from Ref. [48]. The proofs rely on a no-correlation lemma reproduced from Ref. [8], and Proposition 6 provides a continuity bound for the max-relative entropy measure.
Significance. If the main theorem is correct, this is a valuable unifying result: it places previously known conservation-law limits on unitary implementation into a general resource-theoretic framework and yields quantitative bounds with operational error measures. The proof structure is transparent, the axiomatic assumptions are clearly stated, and Proposition 6 is a useful continuity result in its own right. The applications to energy, coherence, entanglement, and quopit magic appear sound. However, the central theorem depends on an externally imported lemma that is not proved here, and the qubit-magic application relies on an additivity inference that is not justified by the cited reference. These issues do not undermine the core theorem but do affect the claimed universality over qubit magic and the self-containedness of the main proof.
major comments (3)
- [Section III / Appendix A, Lemma 7] Theorem 1 rests entirely on the no-correlation lemma: inequalities (A3) and (A4) are the mechanism that converts the implementation error into closeness of the reduced environment states. The lemma is only restated from Ref. [8], which is a preprint by the same authors, and no proof is included in this manuscript. Since Theorem 1 and Corollaries 2 and 3 collapse if this lemma fails, the main derivation is not self-contained. Please either prove Lemma 7 in the paper or provide a published reference containing a complete proof.
- [Section V.D.1] The application of Theorem 4 to qubit magic is not established. The paper claims that R(|ψ⟩⟨ψ|) = log ξ(|ψ⟩) satisfies Property 3' because Ref. [48] showed that the stabilizer extent is multiplicative for tensor products of states supported on up to three qubits. Property 3' requires additivity for arbitrary pure product states, including ρ_S ⊗ ρ_E where ρ_E is an arbitrary N-qubit pure state. The cited three-qubit multiplicativity does not extend by induction, since a tensor product of two such factors is supported on up to six qubits and the cited result does not cover that case. Consequently, the bound on G^p_{U_NC} + L^p_{U_NC} and the claimed Ω(log((G+L)/√ε)) scaling for non-Clifford qubit gates are not supported as written. This is a localized but genuine gap in the claimed universality over qubit magic.
- [Section VI, Eq. (29)] The discussion toward full generality is more limited than it may appear. The statement that exact implementation forces Eq. (29) for any measure with Property 1 is correct, but the subsequent argument only shows that a subadditive monotone would satisfy R(|φ⟩⟨φ|) = R(σ_E'); it does not establish that some measure with Property 1 violates Eq. (29) for a resourceful unitary. Thus the section does not prove a no-go theorem in the absence of additivity; it identifies a condition whose failure would imply impossibility. The authors should make this limitation explicit.
minor comments (5)
- [Title and throughout] The title contains a spacing artifact: "unitar y evolutions" should read "unitary evolutions".
- [Section V.B, after Eq. (22)] In the coherence application, the continuity functions are listed as f1(x) = x, g1(x) = log x, and h1(x) = (1+x)b(x/(1+x)), but Eq. (22) has the dimension d in the logarithmic term. This is presumably g1(d) = log d; the notation should be clarified to avoid confusion between the distance variable and the dimension.
- [Section II, Eq. (9)] The quantity F_e(ρ_S, Λ) is defined as a square root of an entanglement fidelity. This is nonstandard and could be confused with the usual fidelity; a brief comment explaining the choice would improve readability.
- [Section V.D.1] The paper says the stabilizer extent is "multiplicative" while the resource measure R is the logarithm of the extent; the translation to additivity of R is correct only if the cited multiplicativity holds exactly for the required tensor products, which is the issue raised in the major comment.
- [Note added, Section VII] The note about related independent work by Chiribella, Yang, and Renner is acknowledged, but the manuscript does not discuss how the results compare to that work. A brief statement of the relation would be helpful to readers.
Circularity Check
No circularity: the main trade-off theorems are derived from stated axioms plus an independent no-correlation lemma, and no fitted quantity is renamed as a prediction.
full rationale
The central claim, Theorem 1, is a genuine theorem: the bound G_US + L_US <= alpha_L + beta_L follows from the stated Properties 1-3, the definitions of resource generating/losing power, and Lemma 7. Lemma 7 is a general statement about approximate channel implementations and does not assume any resource measure or the target result, so it is not an input equivalent to the output. No parameter is fitted to a subset of data and then presented as a prediction, and no quantity is defined in terms of the very quantity it is used to bound. The applications to energy, coherence, entanglement, and mana are independent consistency checks of the general result. Two flagged concerns are not circularity. First, Appendix A states Lemma 7 from Ref. [8] without proof, so the paper is not fully self-contained at that point; however, the lemma is logically prior and external to the resource-measure framework, so the self-citation is real evidence rather than a circular reduction. Second, Section V.D.1 infers Property 3' for log stabilizer extent from Ref. [48]'s multiplicativity for states supported on at most three qubits, which is a potentially invalid inference and a localized correctness gap, but it is not a constructional circularity. Overall circularity score 0.
Assumptions & free parameters
assumptions (4)
- domain assumption Existence of a resource measure R on the relevant state spaces satisfying Properties 1, 2, and (for Theorem 4) 3'.
- standard math Lemma 7 (no-correlation lemma) from Ref. [8].
- standard math Standard finite-dimensional quantum mechanics, including the Stinespring form of channels, fidelity-distance relations, and trace-distance relations (B1).
- domain assumption For Section VI, composition of free states and partial trace are free operations, and R is a subadditive monotone.
Cite this review
Pith. "Pith review of Universal limitations on implementing resourceful unitary evolutions." pith.science (2026). https://pith.science/paper/RGJ5KF56
@misc{pith2026190901336,
author = {Pith},
title = {Pith review of: Universal limitations on implementing resourceful unitary evolutions},
year = {2026},
howpublished = {\url{https://pith.science/paper/RGJ5KF56}},
note = {Machine review of arXiv:1909.01336}
}
read the original abstract
We derive a trade-off relation between the accuracy of implementing a desired unitary evolution using a restricted set of free unitaries and the size of the assisting system, in terms of the resource generating/losing capacity of the target unitary. In particular, this relation implies that, for any theory equipped with a resource measure satisfying lenient conditions, any resource changing unitary cannot be perfectly implemented by a free unitary applied to a system and an environment if the environment has finite dimensions. Our results are applicable to a wide class of resources including energy, asymmetry, coherence, entanglement, and magic, imposing ultimate limitations inherent in such important physical settings, as well as providing insights into operational restrictions in general resource theories.
Reference graph
Works this paper leans on
-
[8]
Coherence cost for violating conservation laws
H. Tajima, N. Shiraishi, and K. Saito, Coherence cost for violating conservation laws , arXiv e-prints (2019), arXiv:1906.04076 [quant-ph]
work page Pith review arXiv 2019
-
[48]
L. Lami, B. Regula, X. Wang, R. Nichols, A. Winter, and G. Adesso, Gaussian quantum resource theories , Phys. Rev. A 98, 022335 (2018)
2018
-
[1]
relative entropy of magic [ 23], robustness of magic [ 24]), they are not additive for product states in general, which prevents us from apply- ing Theorem
Qubits Although one can consider valid magic monotones de- fined for multiqubit states (e.g. relative entropy of magic [ 23], robustness of magic [ 24]), they are not additive for product states in general, which prevents us from apply- ing Theorem
-
[2]
Quopits For the case when the dimension of the system that each qudit acts on is odd-prime, “mana” was introduced as a magic monotone [ 23]: M(ρ) := log ( ∑ u |Wρ(u)| ) (26) where Wρ(u) is the discrete Wigner function for state ρ [109]. The mana essentially measures the total negativ- ity of the discrete Wigner function, which is motivated by the fact tha...
-
[3]
Ozawa, Uncertainty Principle for Quantum Instruments and Computing , Int
M. Ozawa, Uncertainty Principle for Quantum Instruments and Computing , Int. J. Quantum Inf. 01, 569 (2003)
2003
-
[4]
These results encompass a standard setup where some unit resource state (e.g
with ρE being a pure state. These results encompass a standard setup where some unit resource state (e.g. Bell state for entanglement, uni- form superposition state for coherence), which is usually pure, is prepared in the ancillary system. Although using the unit state as a resource supply appears to be more effective than using a mixed state, interesting...
-
[5]
To this end, consider the stabilizer extent introduced in [ 48]: ξ(|ψ⟩) := min ( ∑ i |ci| ) 2 ⏐ ⏐ ⏐ ⏐ ⏐ ⏐ |ψ⟩ = ∑ i ci |φi⟩ (23) where |φi⟩ are pure stabilizer states
However, Theorem 4 turns out to be useful in this case since there indeed exists a measure de- fined for pure states and additive for pure product mul- tiqubit states. To this end, consider the stabilizer extent introduced in [ 48]: ξ(|ψ⟩) := min ( ∑ i |ci| ) 2 ⏐ ⏐ ⏐ ⏐ ⏐ ⏐ |ψ⟩ = ∑ i ci |φi⟩ (23) where |φi⟩ are pure stabilizer states. The stabil...
-
[6]
˚ Aberg, Catalytic Coherence ,Phys
J. ˚ Aberg, Catalytic Coherence ,Phys. Rev. Lett. 113, 150402 (2014)
2014
Show all 125 references
-
[7]
Tajima, N
H. Tajima, N. Shiraishi, and K. Saito, Uncertainty Relations in Implementation of Unitary Operations , Phys. Rev. Lett. 121, 110403 (2018)
2018
-
[9]
It holds that L(σ(i) AB,UAρ(i) A U † A ⊗σ(i) B ) ≤ 2δUA,(i) I . (A3)
-
[10]
(A4) Moreover, if ρB is a pure state and ΛAB is a unitary operation, one can take a pure state for σ′(0+1) B
There exists a state σ′(0+1) B of B such that L(σ(0) B ,σ ′(0+1) B ) +L(σ′(0+1) B ,σ (1) B ) ≤ 2 √ 2δUA,(0+1) I . (A4) Moreover, if ρB is a pure state and ΛAB is a unitary operation, one can take a pure state for σ′(0+1) B . We are now in a position to prove Theorem 1. Proof. ...
-
[11]
Horodecki, P
R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement , Rev. Mod. Phys. 81, 865 (2009)
2009
-
[12]
(D1) Let Xρ be an optimal solution that achieves ( D1) for state ρ
admits the following dual form [ 113]: maximize log Tr[ ρX] subject to X ≽ 0 Tr[τX ] ≤ 1, ∀τ ∈ STAB. (D1) Let Xρ be an optimal solution that achieves ( D1) for state ρ. Then, we obtain Dmax(σ) ≥ log Tr[σXρ] ≥ log (Tr[ρXρ] − ‖ρ −σ‖1‖Xρ‖∞) = Dmax(ρ) + log ( 1 − ‖ρ −σ‖1‖Xρ‖∞ Tr[ρ...
-
[13]
Then, Property 1 and 3’ of R lead to R(σ(i) SE ) = R(ρ(i) S ) +R(ρE)
and (14) respectively. Then, Property 1 and 3’ of R lead to R(σ(i) SE ) = R(ρ(i) S ) +R(ρE). (C3) and R(USρ(i) S U † S ⊗σ′ E) = R(USρ(i) S U † S) +R(σ′ E). (C4) Combining Property 2, ( C2), ( C3), ( C4), we get |R(ρ(i) S ) +R(ρE) −R(USρ(i) S U † S) −R(σ′ E)| ≤fL(2(1 + √ 2)δUS ...
-
[14]
W. F. Stinespring, Positive Functions on C*-Algebras , Proc. Am. Math. Soc. 6, 211 (1955)
1955
-
[15]
Ozawa, Conservative Quantum Computing , Phys
M. Ozawa, Conservative Quantum Computing , Phys. Rev. Lett. 89, 057902 (2002)
2002
-
[16]
athermality
preserve the Gibbs state τ = exp( −HS/T )/Z where T is the temperature and Z is the partition function of the system. This motivates us to consider the “athermality”, a measure indicating the distance from the Gibbs state to the given state, and es- pecially the free energy is...
-
[17]
Karasawa and M
T. Karasawa and M. Ozawa, Conservation-law-induced quantum limits for physical realizations of the quantum NOT gate , Phys. Rev. A 75, 032324 (2007)
2007
-
[18]
Karasawa, J
T. Karasawa, J. Gea-Banacloche, and M. Ozawa, Gate fidelity of arbitrary single- qubit gates constrained by conservation laws , J. Phys. A: Math. Theor. 42, 225303 (2009)
2009
-
[19]
Brand˜ ao, M
F. Brand˜ ao, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynam- ics, Proc. Natl. Acad. Sci. USA 112, 3275 (2015)
2015
-
[20]
Gallego and L
R. Gallego and L. Aolita, Resource Theory of Steering , Phys. Rev. X 5, 041008 (2015)
2015
-
[21]
Chitambar and G
E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019)
2019
-
[22]
M. B. Plenio and S. Virmani, An introduction to entan- glement measures, Quant. Inf. Comput. 7, 001 (2007)
2007
-
[23]
Veitch, S
V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson, The resource theory of stabilizer quantum computation, New. J. Phys. 16, 013009 (2014)
2014
-
[24]
for pure states, the continuity of stabilizer extent is derived as a special case of this result. It would be also worth noting that the following result holds for the max-relative entropy measure defined for any convex resource theory that includes the maximally mixed state as...
-
[25]
˚ Aberg, Quantifying superposition , (2006), arXiv:quant-ph/0612146
J. ˚ Aberg, Quantifying superposition , (2006), arXiv:quant-ph/0612146
2006 arXiv
-
[26]
Baumgratz, M
T. Baumgratz, M. Cramer, and M. B. Plenio, Quantify- ing Coherence, Phys. Rev. Lett. 113, 140401 (2014)
2014
-
[27]
Streltsov, G
A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource , Rev. Mod. Phys. 89, 041003 (2017)
2017
-
[28]
This makes it even more surprising that Eq
in the equalities, and that the partial trace is a free operation in the last inequalities together with the assumption that R is a monotone under free operations. This makes it even more surprising that Eq. (
-
[29]
We leave the thorough analy- sis on how general the no-go statement can be made for future work
holds for any ρS for resourceful unitary US since it would indi- cate that attaching ancillary states with the same amount of resources to two states with different amount of re- sources would necessarily produce the states with the same amount of resources. We leave the thorou...
-
[30]
Theurer, D
T. Theurer, D. Egloff, L. Zhang, and M. B. Plenio, Quantifying Operations with an Application to Coher- ence, Phys. Rev. Lett. 122, 190405 (2019)
2019
-
[31]
Gour and R
G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: manipulations and mono- tones, New J. Phys. 10, 033023 (2008)
2008
-
[32]
Marvian and R
I. Marvian and R. W. Spekkens, How to quantify coher- ence: Distinguishing speakable and unspeakable notions , Phys. Rev. A 94, 052324 (2016)
2016
-
[33]
F. G. S. L. Brand˜ ao, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Resource The- ory of Quantum States Out of Thermal Equilibrium , Phys. Rev. Lett. 111, 250404 (2013)
2013
-
[34]
Rivas, S
A. Rivas, S. F. Huelga, and M. B. Plenio, Entangle- ment and Non-Markovianity of Quantum Evolutions , Phys. Rev. Lett. 105, 050403 (2010)
2010
-
[35]
Wakakuwa, Operational resource theory of non- markovianity, (2017), arXiv:1709.07248
E. Wakakuwa, Operational resource theory of non- markovianity, (2017), arXiv:1709.07248
2017 arXiv
-
[36]
Howard and E
M. Howard and E. Campbell, Application of a Resource Theory for Magic States to Fault-Tolerant Quantum Computing, Phys. Rev. Lett. 118, 090501 (2017)
2017
-
[37]
M. G. Genoni, M. G. A. Paris, and K. Ba- naszek, Quantifying the non-Gaussian character of a quantum state by quantum relative entropy , Phys. Rev. A 78, 060303 (2008)
2008
-
[38]
Takagi and Q
R. Takagi and Q. Zhuang, Convex resource theory of non-Gaussianity, Phys. Rev. A 97, 062337 (2018)
2018
-
[39]
Albarelli, M
F. Albarelli, M. G. Genoni, M. G. A. Paris, and A. Fer- raro, Resource theory of quantum non-Gaussianity and Wigner negativity, Phys. Rev. A 98, 052350 (2018)
2018
-
[40]
Horodecki and J
M. Horodecki and J. Oppenheim, (Quan- tumness in the context of ) Resource theories , Int. J. Mod. Phys. B 27, 1345019 (2013)
2013
-
[41]
F. G. S. L. Brand˜ ao and G. Gour, Reversible Framework for Quantum Resource Theories , Phys. Rev. Lett. 115, 070503 (2015)
2015
-
[42]
Del Rio, L
L. Del Rio, L. Kraemer, and R. Renner, Resource theo- ries of knowledge , (2015), arXiv:1511.08818
2015 arXiv
-
[43]
Coecke, T
B. Coecke, T. Fritz, and R. W. Spekkens, A Mathemat- ical Theory of Resources , Inf. Comput. 250, 59 (2016)
2016
-
[44]
Z.-W. Liu, X. Hu, and S. Lloyd, Resource Destroying Maps, Phys. Rev. Lett. 118, 060502 (2017)
2017
-
[45]
Gour, Quantum Resource Theories in the Single-Shot Regime, Phys
G. Gour, Quantum Resource Theories in the Single-Shot Regime, Phys. Rev. A 95, 062314 (2017)
2017
-
[46]
Anshu, M.-H
A. Anshu, M.-H. Hsieh, and R. Jain, Quantifying Re- sources in General Resource Theory with Catalysts , Phys. Rev. Lett. 121, 190504 (2018)
2018
-
[47]
Regula, Convex Geometry of Quantum Resource Quantification , J
B. Regula, Convex Geometry of Quantum Resource Quantification , J. Phys. A: Math. Theor. 51, 045303 (2018)
2018
-
[49]
Takagi, B
R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Operational Advantage of Quan- tum Resources in Subchannel Discrimination , Phys. Rev. Lett. 122, 140402 (2019)
2019
-
[50]
L. Li, K. Bu, and Z.-W. Liu, Quantifying the resource content of quantum channels: An operational approach , (2018), arXiv:1812.02572
2018 arXiv
-
[51]
Takagi and B
R. Takagi and B. Regula, General Resource The- ories in Quantum Mechanics and Beyond: Op- erational Characterization via Discrimination Tasks , Phys. Rev. X 9, 031053 (2019)
2019
-
[52]
R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. G¨ uhne, Quantifying Quantum Resources with Conic Program- 12 ming, Phys. Rev. Lett. 122, 130404 (2019)
2019
-
[53]
Z.-W. Liu, K. Bu, and R. Takagi, One- Shot Operational Quantum Resource Theory , Phys. Rev. Lett. 123, 020401 (2019)
2019
-
[54]
Krishnan Vijayan, E
M. Krishnan Vijayan, E. Chitambar, and M.-H. Hsieh, One-shot Distillation in a General Resource Theory , arXiv e-prints (2019), arXiv:1906.04959 [quant-ph]
2019 arXiv
-
[55]
Zanardi, C
P. Zanardi, C. Zalka, and L. Faoro, Entangling Power of Quantum Evolutions , Phys. Rev. A 62, 030301 (2000)
2000
-
[56]
M. G. D ´ ıaz, K. Fang, X. Wang, M. Rosati, M. Skotiniotis, J. Calsamiglia, and A. Winter, Us- ing and reusing coherence to realize quantum processes , Quantum 2, 100 (2018)
2018
-
[57]
J. R. Seddon and E. T. Campbell, Quan- tifying magic for multi-qubit operations , Proc. R. Soc. A 475, 20190251 (2019)
2019
-
[58]
X. Wang, M. M. Wilde, and Y. Su, Quan- tifying the magic of quantum channels , New J. Phys. 21, 103002 (2019)
2019
-
[59]
Vedral, M
V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Quantifying Entanglement , Phys. Rev. Lett. 78, 2275 (1997)
1997
-
[60]
Bravyi, D
S. Bravyi, D. Browne, P. Calpin, E. Campbell, D. Gosset, and M. Howard, Simulation of quan- tum circuits by low-rank stabilizer decompositions , Quantum 3, 181 (2019)
2019
-
[61]
Horodecki and J
M. Horodecki and J. Oppenheim, Fundamental lim- itations for quantum and nanoscale thermodynamics , Nat. Commun. 4, 2059 (2013)
2013
-
[62]
˚ Aberg, Truly work-like work extraction via a single- shot analysis , Nat
J. ˚ Aberg, Truly work-like work extraction via a single- shot analysis , Nat. Commun. 4, 1925 (2013)
2013
-
[63]
Skrzypczyk, A
P. Skrzypczyk, A. J. Short, and S. Popescu, Work ex- traction and thermodynamics for individual quantum systems, Nat. Commun. 5, 4185 (2014)
2014
-
[64]
G. Gour, M. P. M¨ uller, V. Narasimhachar, R. W. Spekkens, and N. Y. Halpern, The resource theory of informational nonequilibrium in thermodynamics , Phys. Rep. 583, 1 (2015)
2015
-
[65]
Tajima, E
H. Tajima, E. Wakakuwa, and T. Ogawa, Large Devia- tion implies First and Second Laws of Thermodynamics , arXiv e-prints (2016), arXiv:1611.06614 [quant-ph]
2016 arXiv
-
[66]
Tasaki, Quantum Statistical Mechanical Derivation of the Second Law of Thermodynamics: A Hybrid Set- ting Approach, Phys
H. Tasaki, Quantum Statistical Mechanical Derivation of the Second Law of Thermodynamics: A Hybrid Set- ting Approach, Phys. Rev. Lett. 116, 170402 (2016)
2016
-
[67]
Shiraishi and H
N. Shiraishi and H. Tajima, Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb- Robinson bound, Phys. Rev. E 96, 022138 (2017)
2017
-
[68]
Morikuni, H
Y. Morikuni, H. Tajima, and N. Hatano, Quantum Jarzynski equality of measurement-based work extrac- tion, Phys. Rev. E 95, 032147 (2017)
2017
-
[69]
Hayashi and H
M. Hayashi and H. Tajima, Measurement- based formulation of quantum heat engines , Phys. Rev. A 95, 032132 (2017)
2017
-
[70]
Hansen, Metric adjusted skew information , Proc
F. Hansen, Metric adjusted skew information , Proc. Natl. Acad. Sci. USA 105, 9909 (2008)
2008
-
[71]
Zhang, B
C. Zhang, B. Yadin, Z.-B. Hou, H. Cao, B.-H. Liu, Y.- F. Huang, R. Maity, V. Vedral, C.-F. Li, G.-C. Guo, and D. Girolami, Detecting metrologically useful asym- metry and entanglement by a few local measurements , Phys. Rev. A 96, 042327 (2017)
2017
-
[72]
Takagi, Skew informations from an opera- tional view via resource theory of asymmetry , Sci
R. Takagi, Skew informations from an opera- tional view via resource theory of asymmetry , Sci. Rep. 9, 14562 (2019)
2019
-
[73]
E. P. Wigner and M. M. Yanase, Information contents of distribution , Proc. Natl. Acad. Sci. USA 49, 910 (1963)
1963
-
[74]
Marvian and R
I. Marvian and R. W. Spekkens, Extending Noether’s theorem by quantifying the asymmetry of quantum states , Nat. Commun. 5, 3821 (2014)
2014
-
[75]
Winter, Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Rel- ative Entropy Distance and Energy Constraints , Commun
A. Winter, Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Rel- ative Entropy Distance and Energy Constraints , Commun. Math. Phys. 347, 291 (2016)
2016
-
[76]
Duan and C
L.-M. Duan and C. Monroe, Colloquium: Quantum networks with trapped ions , Rev. Mod. Phys. 82, 1209 (2010)
2010
-
[77]
Pirker, J
A. Pirker, J. Walln¨ ofer, and W. D¨ ur, Mod- ular architectures for quantum networks , New. J. Phys. 20, 053054 (2018)
2018
-
[78]
Eisert, K
J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Optimal local implementation of nonlocal quantum gates , Phys. Rev. A 62, 052317 (2000)
2000
-
[79]
Soeda, P
A. Soeda, P. S. Turner, and M. Murao, Entanglement Cost of Implementing Controlled-Unitary Operations , Phys. Rev. Lett. 107, 180501 (2011)
2011
-
[80]
Chen and L
L. Chen and L. Yu, Nonlocal and con- trolled unitary operators of Schmidt rank three , Phys. Rev. A 89, 062326 (2014)
2014
-
[81]
Chen and L
L. Chen and L. Yu, Entanglement cost and entangling power of bipartite unitary and permutation operators , Phys. Rev. A 93, 042331 (2016)
2016
-
[82]
Wakakuwa, A
E. Wakakuwa, A. Soeda, and M. Mu- rao, A Coding Theorem for Bipartite Uni- taries in Distributed Quantum Computation , IEEE Trans. Inf. Theory 63, 5372 (2017)
2017
-
[83]
Wakakuwa, A
E. Wakakuwa, A. Soeda, and M. Murao, Com- plexity of Causal Order Structure in Distributed Quantum Information Processing: More Rounds of Classical Communication Reduce Entanglement Cost , Phys. Rev. Lett. 122, 190502 (2019)
2019
-
[84]
Pirandola, R
S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Fundamental limits of repeaterless quantum communica- tions, Nat. Commun. 8, 15043 (2017)
2017
-
[85]
One could alternatively argue the impossibility of im- plementing entangling gates only using local operations and shared entanglement by noting that no signaling is allowed under this setup
-
[86]
K. G. H. Vollbrecht and R. F. Werner, Entanglement measures under symmetry , Phys. Rev. A 64, 062307 (2001)
2001
-
[87]
Datta, Max- Relative Entropy of Entanglement, alias Log Robustness, Int
N. Datta, Max- Relative Entropy of Entanglement, alias Log Robustness, Int. J. Quantum Inf. 07, 475 (2009)
2009
-
[88]
Vidal and R
G. Vidal and R. Tarrach, Robustness of entanglement , Phys. Rev. A 59, 141 (1999)
1999
-
[89]
Squashed en- tanglement
M. Christandl and A. Winter, “Squashed en- tanglement”: An additive entanglement measure , 13 J. Math. Phys. 45, 829 (2004)
2004
-
[90]
Alicki and M
R. Alicki and M. Fannes, Continu- ity of quantum conditional information , J. Phys. A: Math. Gen. 37, L55 (2004)
2004
-
[91]
D. Yang, M. Horodecki, and Z. D. Wang, An Ad- ditive and Operational Entanglement Measure: Conditional Entanglement of Mutual Information , Phys. Rev. Lett. 101, 140501 (2008)
2008
-
[92]
P. W. Shor, Fault-tolerant quantum computation, in Proceedings of 37th Conference on Foundations of Computer S cience (1996) pp. 56–65
1996
-
[93]
Preskill, Fault-tolerant quantum computation, in Introduction to Quantum Computation and Information (1998) pp
J. Preskill, Fault-tolerant quantum computation, in Introduction to Quantum Computation and Information (1998) pp. 213–269
1998
-
[94]
A. M. Steane, Error Correcting Codes in Quantum The- ory, Phys. Rev. Lett. 77, 793 (1996)
1996
-
[95]
P. W. Shor, Scheme for reducing deco- herence in quantum computer memory , Phys. Rev. A 52, R2493 (1995)
1995
-
[96]
A. M. Steane, Active Stabilization, Quantum Computation, and Quantum State Synthesis , Phys. Rev. Lett. 78, 2252 (1997)
1997
-
[97]
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation , Phys. Rev. A 86, 032324 (2012)
2012
-
[98]
Bombin and M
H. Bombin and M. A. Martin- Delgado, Topological Quantum Distillation , Phys. Rev. Lett. 97, 180501 (2006)
2006
-
[99]
Gottesman and I
D. Gottesman and I. L. Chuang, Demonstrat- ing the viability of universal quantum computa- tion using teleportation and single-qubit operations , Nature 402, 390 (1999)
1999
-
[100]
Bravyi and A
S. Bravyi and A. Kitaev, Universal quantum com- putation with ideal Clifford gates and noisy ancillas , Phys. Rev. A 71, 022316 (2005)
2005
-
[101]
Bravyi and J
S. Bravyi and J. Haah, Magic-state distillation with low overhead, Phys. Rev. A 86, 052329 (2012)
2012
-
[102]
A. G. Fowler, S. J. Devitt, and C. Jones, Surface code implementation of block code state distillation , Sci. Rep. 3, 1939 (2013)
2013
-
[103]
Jones, Multilevel distillation of magic states for quan- tum computing , Phys
C. Jones, Multilevel distillation of magic states for quan- tum computing , Phys. Rev. A 87, 042305 (2013)
2013
-
[104]
Duclos-Cianci and K
G. Duclos-Cianci and K. M. Svore, Distillation of nonstabilizer states for universal quantum computation , Phys. Rev. A 88, 042325 (2013)
2013
-
[105]
Duclos-Cianci and D
G. Duclos-Cianci and D. Poulin, Reducing the quantum- computing overhead with complex gate distillation , Phys. Rev. A 91, 042315 (2015)
2015
-
[106]
E. T. Campbell and M. Howard, Unified frame- work for magic state distillation and multi- qubit gate synthesis with reduced resource cost , Phys. Rev. A 95, 022316 (2017)
2017
-
[107]
O’Gorman and E
J. O’Gorman and E. T. Campbell, Quantum computation with realistic magic-state factories , Phys. Rev. A 95, 032338 (2017)
2017
-
[108]
Haah and M
J. Haah and M. B. Hastings, Codes and Proto- cols for Distilling T , controlled- S, and Toffoli Gates , Quantum 2, 71 (2018)
2018
-
[109]
E. T. Campbell and M. Howard, Magic state parity-checker with pre-distilled components , Quantum 2, 56 (2018)
2018
-
[110]
A. G. Fowler and C. Gidney, Low overhead quantum computation using lattice surgery , arXiv e-prints (2018), arXiv:1808.06709 [quant-ph]
2018 arXiv
-
[111]
Gidney and A
C. Gidney and A. G. Fowler, Efficient magic state fac- tories with a catalyzed |CCZ ⟩ to 2|T ⟩ transformation, Quantum 3, 135 (2019)
2019
-
[112]
Litinski, Magic State Distillation: Not as Costly as You Think , Quantum 3, 205 (2019)
D. Litinski, Magic State Distillation: Not as Costly as You Think , Quantum 3, 205 (2019)
2019
-
[113]
Paetznick and B
A. Paetznick and B. W. Reichardt, Univer- sal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction , Phys. Rev. Lett. 111, 090505 (2013)
2013
-
[114]
J. T. Anderson, G. Duclos-Cianci, and D. Poulin, Fault-Tolerant Conversion between the Steane and Reed-Muller Quantum Codes , Phys. Rev. Lett. 113, 080501 (2014)
2014
-
[115]
Bomb ´ ın,Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes , New
H. Bomb ´ ın,Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes , New. J. Phys. 17, 083002 (2015)
2015
-
[116]
Jochym-O’Connor and R
T. Jochym-O’Connor and R. Laflamme, Using Con- catenated Quantum Codes for Universal Fault-Tolerant Quantum Gates , Phys. Rev. Lett. 112, 010505 (2014)
2014
-
[117]
Nikahd, M
E. Nikahd, M. Sedighi, and M. Saheb Zamani, Nonuni- form code concatenation for universal fault-tolerant quantum computing , Phys. Rev. A 96, 032337 (2017)
2017
-
[118]
Chamberland, T
C. Chamberland, T. Jochym-O’Connor, and R. Laflamme, Thresholds for Universal Concatenated Quantum Codes , Phys. Rev. Lett. 117, 010501 (2016)
2016
-
[119]
T. J. Yoder, R. Takagi, and I. L. Chuang, Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes , Phys. Rev. X 6, 031039 (2016)
2016
-
[120]
Takagi, T
R. Takagi, T. J. Yoder, and I. L. Chuang, Error rates and resource overheads of encoded three-qubit gates , Phys. Rev. A 96, 042302 (2017)
2017
-
[121]
Gross, Hudson ’s theorem for finite-dimensional quan- tum systems , J
D. Gross, Hudson ’s theorem for finite-dimensional quan- tum systems , J. Math. Phys. 47, 122107 (2006)
2006
-
[122]
Veitch, C
V. Veitch, C. Ferrie, D. Gross, and J. Emerson, Negative quasi-probability as a resource for quantum computation , New. J. Phys. 14, 113011 (2012)
2012
-
[123]
Chiribella, Y
G. Chiribella, Y. Yang, and R. Renner, The energy re- quirement of quantum processors, arXiv e-prints (2019), arXiv:1908.10884 [quant-ph]
2019 arXiv
-
[124]
C. A. Fuchs and J. van de Graaf, Cryptographic dis- tinguishability measures for quantum-mechanical states , IEEE Trans. Inf. Theory 45, 1216 (1999)
1999
-
[125]
Boyd and L
S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, New York, 2004)
2004
Reviewed August 14, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.