A hierarchy of thermodynamically consistent quantum operations

Fereshte Shahbeigi; M. Hamed Mohammady

A hierarchy of thermodynamically consistent quantum operations

T0 review · 0 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Strictly positive maps are exactly the weak-third-law operations.

desk verdict A clean, honest hierarchy of thermodynamically consistent operations and instruments; the main caveat is the loaded modeling assumption that 'full consistency' means arbitrary bistochastic interactions, but the results are robust enough that it deserves a serious referee. read the letter →

arxiv 2505.23360 v1 pith:3QFA4BBH submitted 2025-05-29 quant-ph

Fereshte Shahbeigi , M. Hamed Mohammady This is my paper

classification quant-ph

keywords quantumoperationsthirdlawofthermodynamicsstrictlypositivemapsranknon-decreasingchannelsbistochasticinstrumentsPOVMsnon-disturbingmeasurements

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks which quantum operations and measurements could actually be implemented if the only constraints beyond quantum theory are the laws of thermodynamics. It builds a three-tier hierarchy of thermodynamically consistent processes, each requiring the apparatus to start in a strictly positive (full-rank) state and differing only in the allowed system-apparatus interaction: strictly positive maps for the weak third law, rank non-decreasing maps for the strong third law, and bistochastic channels for the second and third laws together. The main results convert each thermodynamic principle into a property of the operation itself: a channel obeys the weak third law if and only if it is strictly positive, obeys the strong third law if and only if it is rank non-decreasing, and full consistency implies that the channel has a strictly positive fixed state. The paper further shows that no POVM is ruled out by thermodynamics, but the realizable state-update rules become increasingly restricted: repeatability is forbidden by the weak third law, ideality and value reproducibility by the strong third law, and first-kind measurements survive full consistency only for completely unsharp, mutually commuting effects.

What carries the argument

The central object is the three-tier hierarchy of processes (Definition 2), in which the apparatus state is always strictly positive and the interaction channel is required to be strictly positive (I), rank non-decreasing (II), or bistochastic (III). The hierarchy isolates a single thermodynamic principle per tier, letting the authors attribute each forbidden measurement property to a specific law. The proofs use map-theoretic facts: strict positivity is detected through the null space of the dual map; rank non-decreasing maps are characterized by approximate operator scaling; and bistochasticity makes the classical action of a channel a doubly stochastic matrix, whose irreducible blocks, via Perron-Frobenius theory, force fixed states to have full rank. Together these facts carry the equivalence theorems for operations and channels and the fixed-state theorem for fully consistent channels.

What would settle it

In dimension two or higher, search for a channel of the form Phi(rho) = tr_A[E(rho ⊗ xi)] with xi strictly positive and E bistochastic such that every fixed state of Phi is rank-deficient. Theorem 4.3 asserts that no such channel exists, so a single counterexample would refute the characterization of fully consistent channels; equivalently, an operation in O_I that is not strictly positive, or a channel in O_II that decreases rank, would refute Theorems 4.1 and 4.2.

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Extended reading notes

Core claim

The central discovery is a dictionary between thermodynamic principles and linear-algebraic properties of completely positive maps. Under the weak third law, a nonzero operation is realizable if and only if it is strictly positive; under the strong third law, a channel is realizable if and only if it is rank non-decreasing, and the same holds for operations compatible with completely unsharp effects; under full consistency, every channel must be rank non-decreasing and must have a strictly positive fixed state. Because the fixed-point algebra of such a channel is a von Neumann algebra, first-kind measurements require unsharp effects and, when the second law is imposed, commutativity of those effects. The same framework shows that every effect is measurable in a thermodynamically consistent way through fully disturbing instruments, so thermodynamics restricts state-update rules rather than the POVMs themselves.

Load-bearing premise

The characterization of fully consistent channels assumes that an adiabatically isolated system-apparatus compound may evolve by any bistochastic (entropy-nonincreasing) channel rather than only by unitary channels; if the second law actually forced unitarity or a narrower class, the class O_III and its strictly-positive-fixed-state theorem would describe only a subset of thermodynamically allowed processes.

Editorial extensions

If this is right

Every fully consistent channel preserves a strictly positive, generally non-equilibrium, steady state, generalizing the thermal channels' preservation of the thermal equilibrium state.
The third law, not the second, is responsible for most measurement no-go results: repeatability already fails under the weak third law, while ideality and value reproducibility fail under the strong third law.
Every POVM remains measurable in a thermodynamically consistent way, but only through fully disturbing instruments; the allowed state-update rules depend on which tier is imposed.
First-kind measurements under the strong third law must be completely unsharp, with every effect strictly between zero and the identity; full consistency additionally requires the effects to commute.
The thermodynamically consistent operation sets are convex monoids whose closure is the full set of operations, so every operation can be approximated by a fully consistent one, while operations with strictly positive Choi operators lie inside the fully consistent class.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the strictly-positive-fixed-state property is taken as the operational signature of full consistency, resource measures for quantum thermodynamics could be phrased as distances from the fixed-state set, giving a quantitative trade-off the paper leaves open.
A natural numerical extension is to sample channels generated by bistochastic dilations in low dimensions and estimate how large the gap is between fully consistent channels and merely rank non-decreasing channels.
The authors' choice of bistochastic rather than unitary interactions leaves open whether adding a conserved additive quantity would reduce first-kind measurements to observables commuting with the system part of that quantity, a corollary hinted at by the conservation-law remark.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a genuinely useful paper. It shows that the weak third law forbids repeatability, the strong third law forbids ideality and value reproducibility, and first-kindness requires unsharp effects, with commutativity only under full consistency. The characterizations of channels—weak third law iff strictly positive, strong third law iff rank non-decreasing, full consistency implies a strictly positive fixed state—are proven in detail with standard tools. The sufficiency proofs are new, and the tensor-extension result for rank non-decreasing maps (Prop B.1) closes a gap that needed closing for the physics to make sense.

The main soft spot is exactly the one you flagged: the set OIII is defined via bistochastic interactions, and that is an assumption about what the second law allows, not a derivation. The authors are explicit about this, but it means the phrase 'fully consistent with thermodynamics' is doing some interpretive work. If you hold the line that the second law forces unitarity, the set is too big. That said, the no-go results in Theorem 4.4 and the strictly-positive-fixed-state theorem are monotone under shrinking the allowed interactions, so the hierarchy's main conclusions survive even under the stricter reading. Proposition 4.1's density argument also works with unitary interactions alone.

Otherwise the proofs look sound. I checked the potentially handwavy step in Prop 4.1 about the interior: for a convex dense subset, the interior containment does follow from standard convexity facts, even though the text's 'no punctures' phrasing is terse. The proof of Theorem 4.4(v) is in the appendix, and it is complete. The authors also state clearly which classes are only partially characterized.

This paper is for anyone working on quantum measurement theory and its thermodynamic constraints. It's a good candidate for a reading group because the central modeling assumption is genuinely debatable. I'd send it to a serious referee, with the explicit instruction that the bistochastic-versus-unitary issue be weighed. I would also cite it: the characterizations are clean and likely to be useful regardless of how that assumption settles.

Referee Report

0 major / 5 minor

Summary. The paper introduces a hierarchy of quantum operations and instruments constrained by (I) the weak third law, (II) the strong third law, and (III) full consistency with thermodynamics. In each class the apparatus is required to start in a strictly positive state, while the interaction channel is required to be strictly positive, rank non-decreasing, or bistochastic. For channels, the authors prove that weak consistency is equivalent to strict positivity (Theorem 4.1), strong consistency is equivalent to rank non-decreasing (Theorem 4.2 and Corollary F.1), and full consistency implies the existence of a strictly positive fixed state (Theorem 4.3). They also show that the fully consistent operations are dense in the set of all operations (Proposition 4.1). For instruments, they prove that repeatability, ideality, value reproducibility, and first-kindness are increasingly restricted, with first-kind measurements requiring completely unsharp effects and, under full consistency, commutativity (Theorem 4.4). Detailed proofs are provided in the appendices using Stinespring-Naimark-Ozawa dilations, Schauder-Tychonoff, Perron-Frobenius, and von Neumann algebra fixed-point structure.

Significance. Assuming the stated formalization, the paper is a useful conceptual and technical contribution. It unifies and sharpens earlier results on thermodynamically constrained measurements, gives exact characterizations for the weak and strong third-law classes of channels, and provides clean no-go constraints for non-disturbing measurements. The appendices contain rigorous proofs, including a nontrivial complete-rank-non-decreasing extension lemma (Proposition B.1) and a detailed fixed-state analysis for fully consistent channels (Proposition G.1). The paper is also honest about its main modeling assumption, namely that a thermodynamically closed system-apparatus compound may evolve under arbitrary bistochastic channels rather than only unitary ones; the unitary alternative is explicitly flagged. This conditionality is a physical-interpretation caveat rather than an internal mathematical inconsistency, and it affects only the claim that the set OIII represents 'full consistency with thermodynamics' in an unconditional sense.

minor comments (5)

[Abstract and Section 3, Definition 2(III)] The physical scope of 'fully consistent with thermodynamics' depends on the assumption that a thermodynamically closed compound may undergo an arbitrary bistochastic channel. The paper is explicit about this premise and about the unitary alternative, but the abstract and conclusions present it as the definition of full consistency. I recommend adding one sentence in the abstract and in the Discussion stating that this is a modeling choice and that replacing bistochastic interactions by unitary ones would change the set OIII and hence some conclusions.
[Proposition 4.1] The parenthetical 'i.e., operations with a strictly positive Choi operator' is not accurate: the identity channel has a positive-definite Choi operator but lies on the boundary of the trace-non-increasing set O(H), not in its interior. The proof of the proposition does not rely on this equivalence, but the statement should be rephrased, for example by saying that operations with strictly positive Choi operator provide a convenient subset whose closure properties imply the density claim.
[Definition 4 and Theorem 4.4] The notation for the three instrument classes is hard to distinguish in plain text, especially 'II', 'III', and 'IIII'. Please use superscripted labels such as I^{(I)}, I^{(II)}, I^{(III)} throughout, or otherwise clearly differentiate the weak, strong, and full classes.
[Appendix G, Proposition G.1] The construction of the 'maximal' set of orthocomplete projections {P_beta} should explicitly state that a maximal refinement exists because the Hilbert space is finite-dimensional. Currently the proof argues by contradiction and splitting, but an explicit well-foundedness statement would make the argument easier to follow.
[Section 3, Full consistency with thermodynamics] The sentence 'bistochastic channels are precisely those that do not decrease the entropy of any state' is a known but nontrivial fact for quantum channels. Since it is load-bearing for the motivation of Definition 2(III), please give a precise statement or a more specific citation than the general reference [5].

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the hierarchy theorems are proved from the stated process definitions, not assumed; the bistochastic premise is an explicit modeling choice, not a hidden input.

full rationale

The paper's central equivalences are genuine theorems relative to Definition 2. Theorem 4.1 is proved in both directions: necessity follows from strict positivity of the joint channel and apparatus state (Lemma E.1, re-proving Lemma D.1 of Ref. [33]), and sufficiency is a constructive process using E = Σ I_x ⊗ tr[·]|x⟩⟨x|. Theorem 4.2 proves the iff for channels via rank inequalities (Lemma F.2) and the tensor product property (Proposition B.1), with sufficiency by E = Φ⊗id. Theorem 4.3 is an independent Perron-Frobenius/classical-action argument (Proposition G.1), not a restatement of bistochasticity of Φ itself. Theorem 4.4's no-go statements are proved from the definitions, with prior results such as Ref. [33] used as lemmas that are also re-derived or extended in the appendices. The identification of the weak/strong third law with strict positivity/rank non-decreasing is a stated physical premise, and the 'full consistency' set depends on the explicitly flagged assumption that thermodynamically closed compounds may evolve by any bistochastic channel (Sec. 3). That assumption is contestable, but contesting it is a correctness/scope objection, not a circularity: the paper does not derive it from its own conclusions, and it openly notes that unitarity is sufficient but not necessary. Self-citations are load-bearing only in the sense of citing prior published lemmas; they are not used as unproven premises that already contain the target results. Hence no step reduces by construction to its inputs.

Assumptions & free parameters 0 free parameters · 8 assumptions · 0 invented entities

No fitted parameters or invented physical entities. The hierarchy (weak third law, strong third law, full consistency) is a classification scheme, not a new ontological object. The central claims rest on the domain assumptions listed above.

assumptions (8)

domain assumption Finite-dimensional Hilbert spaces
Stated at the start of Sec. 2.1; all fixed-point, Perron-Frobenius, and von Neumann algebra arguments rely on finite dimensionality.
domain assumption Weak third law = strict positivity of apparatus state and interaction channel
Definition 2(I) and Sec. 3; this is a modeling choice, not derived from a microscopic third law.
domain assumption Strong third law = rank non-decreasing interaction channel
Definition 2(II) and Sec. 3; the paper itself notes this is one of two possible formalizations.
domain assumption Second law = bistochastic interaction channel
Definition 2(III) and Sec. 3: 'the interaction is consistent with the second law if and only if it is described by a bistochastic channel.' This is the load-bearing assumption for OIII.
standard math Stinespring-Naimark-Ozawa dilation theorem
Used in Eq. (1), Prop 4.1, and Appendix E to represent operations and to construct processes.
standard math Schauder-Tychonoff fixed point theorem
Used in Sec. 2.3 and Appendix G to guarantee every channel has a fixed state.
standard math Perron-Frobenius theorem for irreducible stochastic matrices
Used in Lemma G.3 to conclude a fixed state of an irreducible classical action is strictly positive.
standard math Fixed-point set of a dual channel with a strictly positive fixed state is a von Neumann algebra
Used in Sec. 4.1 and Theorem 4.4(vi) via Refs. [43,44].

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Pith. "Pith review of A hierarchy of thermodynamically consistent quantum operations." pith.science (2026). https://pith.science/paper/3QFA4BBH

@misc{pith2026250523360,
  author       = {Pith},
  title        = {Pith review of: A hierarchy of thermodynamically consistent quantum operations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3QFA4BBH}},
  note         = {Machine review of arXiv:2505.23360}
}

abstract

In order to determine what quantum operations and measurements are consistent with the laws of thermodynamics, one must start by allowing all processes allowed by the framework of quantum theory, and then impose the laws of thermodynamics as a set of constraints. Here, we consider a hierarchy of quantum operations and measurements that are consistent with ($I$) the weak third law, ($II$) the strong third law, and ($III$) both the second and the third laws of thermodynamics, i.e., operations and measurements that are fully consistent with thermodynamics. Such characterisation allows us to identify which particular thermodynamic principle is responsible for the (un)attainability of a given quantum operation or measurement. In the case of channels, i.e., trace-preserving operations, we show that a channel belongs to ($I$) and ($II$) if and only if it is strictly positive and rank non-decreasing, respectively, whereas a channel belongs to ($III$) only if it is rank non-decreasing and does not perturb a strictly positive state. On the other hand, while thermodynamics does not preclude the measurability of any POVM, the realisable state-update rules for measurements are increasingly restricted as we go from ($I$) to ($III$).

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Works this paper leans on

55 extracted references · 40 canonical work pages

[1]

von Neumann, Mathematical Foundations of Quantum Mechanics: New Edition (Princeton University Press, 2018)

J. von Neumann, Mathematical Foundations of Quantum Mechanics: New Edition (Princeton University Press, 2018)

2018
[2]

Neumark, Spectral functions of a symmetric operator, Izv

M. Neumark, Spectral functions of a symmetric operator, Izv. Math. 4, 227 (1940)

1940
[3]

W. F. Stinespring, Positive Functions on C* -Algebras, Proc. Am. Math. Soc. 6, 211 (1955)

1955
[4]

Ozawa, Quantum measuring processes of continuous observables, J

M. Ozawa, Quantum measuring processes of continuous observables, J. Math. Phys. 25, 79 (1984)

1984
[5]

DISCUSSION This work generalizes and unifies previous works relating to the thermodynamic consistency of quantum operations and measurements. In the conventional framework, thermodynamically consistent operations—interpreted as operations consuming only finite thermodynamic resources—are considered as those that are implementable via a unitary interaction...

work page 2023
[6]

Purves and A

T. Purves and A. J. Short, Channels, measurements, and postselection in quantum thermodynamics, Phys. Rev. E 104, 014111 (2021)

2021
[7]

Minagawa, M

S. Minagawa, M. H. Mohammady, K. Sakai, K. Kato, and F. Buscemi, Universal validity of the second law of information thermodynamics, npj Quantum Inf. 11, 18 (2025)

2025
[8]

L. J. Schulman, T. Mor, and Y. Weinstein, Physical Limits of Heat-Bath Algorithmic Cooling, Phys. Rev. Lett. 94, 120501 (2005)

2005

Show all 55 references

[9]

A. E. Allahverdyan, K. V. Hovhannisyan, D. Janzing, and G. Mahler, Thermodynamic limits of dynamic cooling, Phys. Rev. E 84, 041109 (2011)

2011
[10]

Ticozzi and L

F. Ticozzi and L. Viola, Quantum resources for purification and cooling: fundamental limits and opportunities, Sci. Rep. 4, 5192 (2015)

2015
[11]

Masanes and J

L. Masanes and J. Oppenheim, A general derivation and quantification of the third law of thermodynamics, Nat. Commun. 8, 14538 (2017)

2017
[12]

Wilming and R

H. Wilming and R. Gallego, Third Law of Thermodynamics as a Single Inequality, Phys. Rev. X 7, 041033 (2017)

2017
[13]

Scharlau and M

J. Scharlau and M. P. Mueller, Quantum Horn’s lemma, finite heat baths, and the third law of thermodynamics, Quantum 2, 54 (2018)

2018
[14]

Freitas, R

N. Freitas, R. Gallego, L. Masanes, and J. P. Paz, Cooling to Absolute Zero: The Unattainability Principle, in Thermodyn. Quantum Regime Fundam. Theor. Phys. , Vol. 195, edited by F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer International Publishing, 20...

2018
[15]

Taranto, F

P. Taranto, F. Bakhshinezhad, A. Bluhm, R. Silva, N. Friis, M. P. Lock, G. Vitagliano, F. C. Binder, T. Debarba, E. Schwarzhans, F. Clivaz, and M. Huber, Landauer Versus Nernst: What is the True Cost of Cooling a Quantum System?, PRX Quantum 4, 010332 (2023)

2023
[16]

Taranto, P

P. Taranto, P. Lipka-Bartosik, N. A. Rodr´ıguez-Briones, M. Perarnau-Llobet, N. Friis, M. Huber, and P. Bakhshinezhad, Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic Geometry, Phys. Rev. Lett. 134, 070401 (2025)

2025
[17]

Horodecki and J

M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013)

2013
[18]

Navascu ´es and L

M. Navascu ´es and L. P. Garc ´ıa-Pintos, Nonthermal Quantum Channels as a Thermodynamical Resource, Phys. Rev. Lett. 115, 1 (2015)

2015
[19]

Brand ˜ao, M

F. Brand ˜ao, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynamics, Proc. Natl. Acad. Sci. 112, 3275 (2015)

2015
[20]

Perry, P

C. Perry, P. ´Cwikli´nski, J. Anders, M. Horodecki, and J. Oppenheim, A Sufficient Set of Experimentally Implementable Thermal Operations for Small Systems, Phys. Rev. X 8, 041049 (2018)

2018
[21]

Lostaglio, ´A

M. Lostaglio, ´A. M. Alhambra, and C. Perry, Elementary Thermal Operations, Quantum 2, 52 (2018)

2018
[22]

Mazurek and M

P. Mazurek and M. Horodecki, Decomposability and convex structure of thermal processes, New J. Phys. 20, 053040 (2018)

2018
[23]

M. H. Mohammady, Thermodynamically free quantum measurements, J. Phys. A Math. Theor. 55, 505304 (2022)

2022
[24]

B. M. Terhal, I. L. Chuang, D. P. DiVincenzo, M. Grassl, and J. A. Smolin, Simulating quantum operations with mixed environments, Phys. Rev. A 60, 881 (1999)

1999
[25]

Zalka and E

C. Zalka and E. Rieffel, Quantum operations that cannot be implemented using a small mixed environment, J. Math. Phys. 43, 4376 (2002)

2002
[26]

˙Zyczkowski and I

K. ˙Zyczkowski and I. Bengtsson, On Duality between Quantum Maps and Quantum States, Open Syst. Inf. Dyn. 11, 3 (2004)

2004
[27]

G. Gour, M. P. M ¨uller, V. Narasimhachar, R. W. Spekkens, and N. Yunger Halpern, The resource theory of informational nonequilibrium in thermodynamics, Phys. Rep. 583, 1 (2015)

2015
[28]

Guryanova, N

Y. Guryanova, N. Friis, and M. Huber, Ideal Projective Measurements Have Infinite Resource Costs, Quantum 4, 222 (2020)

2020
[29]

Panda, F

A. Panda, F. C. Binder, and S. Vinjanampathy, Nonideal measurement heat engines, Phys. Rev. A 108, 062214 (2023)

2023
[30]

Vetrivelan, A

M. Vetrivelan, A. Panda, and S. Vinjanampathy, Metrology in the presence of thermodynamically consistent measurements, Phys. Rev. A 109, 052610 (2024)

2024
[31]

Debarba, M

T. Debarba, M. Huber, and N. Friis, Unknown measurement statistics cannot be redundantly copied using finite resources, 34 (2024), arXiv:2403.07660

2024 arXiv
[32]

M. H. Mohammady and F. Buscemi, The thermodynamic trilemma of efficient measurements, (2025), arXiv:2502.14136

2025 arXiv
[33]

vom Ende, Strict positivity and D -majorization, Linear Multilinear Algebr

F. vom Ende, Strict positivity and D -majorization, Linear Multilinear Algebr. 70, 4023 (2022)

2022
[34]

M. H. Mohammady and T. Miyadera, Quantum measurements constrained by the third law of thermodynamics, Phys. Rev. A 107, 022406 (2023)

2023
[35]

Busch, M

P. Busch, M. Grabowski, and P. J. Lahti, Operational Quantum Physics , Lecture Notes in Physics Monographs, Vol. 31 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1995)

1995
[36]

Busch, P

P. Busch, P. J. Lahti, and Peter Mittelstaedt, The Quantum Theory of Measurement , Lecture Notes in Physics Monographs, Vol. 2 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1996)

1996
[37]

Heinosaari and M

T. Heinosaari and M. Ziman, The Mathematical language of Quantum Theory (Cambridge University Press, Cambridge, 2011)

2011
[38]

M. M. Wolf, Quantum channels and operations: Guided tour (2012)

2012
[39]

Busch, P

P. Busch, P. Lahti, J.-P. Pellonp ¨a¨a, and K. Ylinen, Quantum Measurement , Theoretical and Mathematical Physics (Springer International Publishing, Cham, 2016)

2016
[40]

Hayashi, Quantum Information Theory , Graduate Texts in Physics (Springer Berlin Heidelberg, Berlin, Heidelberg, 2017)

M. Hayashi, Quantum Information Theory , Graduate Texts in Physics (Springer Berlin Heidelberg, Berlin, Heidelberg, 2017)

2017
[41]

Pata, Fixed Point Theorems and Applications , UNITEXT, Vol

V. Pata, Fixed Point Theorems and Applications , UNITEXT, Vol. 116 (Springer International Publishing, Cham, 2019)

2019
[42]

Tumulka and J

R. Tumulka and J. Weixler, Fixed Points of Completely Positive Trace-Preserving Maps in Infinite Dimension, (2024), arXiv:2411.14800

2024 arXiv
[43]

M. H. Mohammady and T. Miyadera, Erratum: Quantum measurements constrained by the third law of thermodynamics [Phys. Rev. A 107 , 022406 (2023)], Phys. Rev. A 110, 029901(E) (2024)

2023
[44]

Bratteli, P

O. Bratteli, P. E. T. Jorgensen, A. Kishimoto, and R. F. Werner, Pure states on Od, J. Oper. Theory 43, 97 (1997)

1997
[45]

Arias, A

A. Arias, A. Gheondea, and S. Gudder, Fixed points of quantum operations, J. Math. Phys. 43, 5872 (2002)

2002
[46]

No Information Without Disturbance

P. Busch, “No Information Without Disturbance”: Quantum Limitations of Measurement, in Quantum Reality, Relativ. Causality, Closing Epistemic Circ. (Springer, Dordrecht, 2009) pp. 229–256

2009
[47]

Heinosaari and M

T. Heinosaari and M. M. Wolf, Nondisturbing quantum measurements, J. Math. Phys. 51, 092201 (2010)

2010
[48]

M. H. Mohammady, T. Miyadera, and L. Loveridge, Measurement disturbance and conservation laws in quantum mechanics, Quantum 7, 1033 (2023)

2023
[49]

Gurvits, Classical deterministic complexity of Edmonds’ Problem and quantum entanglement, in Proc

L. Gurvits, Classical deterministic complexity of Edmonds’ Problem and quantum entanglement, in Proc. thirty-fifth Annu. ACM Symp. Theory Comput. (ACM, New York, NY, USA, 2003) pp. 10–19, arXiv:0303055 [quant-ph]

2003
[50]

A. S. Holevo, Complementary Channels and the Additivity Problem, Theory Probab. Its Appl. 51, 92 (2007)

2007
[51]

van Dam and P

W. van Dam and P. Hayden, Renyi-entropic bounds on quantum communication, (2002), arXiv:0204093 [quant-ph]

2002
[52]

Perfect and L

H. Perfect and L. Mirsky, Spectral properties of doubly-stochastic matrices, Monatshefte f ¨ur Math. 69, 35 (1965)

1965
[53]

Serre, Matrices: Theory and Applications , Graduate Texts in Mathematics (Springer New York, 2010)

D. Serre, Matrices: Theory and Applications , Graduate Texts in Mathematics (Springer New York, 2010)

2010
[54]

Lindblad, A general no-cloning theorem, Lett

G. Lindblad, A general no-cloning theorem, Lett. Math. Phys. 47, 189 (1999)

1999
[55]

Choi, A schwarz inequality for positive linear maps on C*-algebras, Illinois J

M.-D. Choi, A schwarz inequality for positive linear maps on C*-algebras, Illinois J. Math. 18, 565 (1974)

1974

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

von Neumann, Mathematical Foundations of Quantum Mechanics: New Edition (Princeton University Press, 2018)

J. von Neumann, Mathematical Foundations of Quantum Mechanics: New Edition (Princeton University Press, 2018)

2018

[2] [2]

Neumark, Spectral functions of a symmetric operator, Izv

M. Neumark, Spectral functions of a symmetric operator, Izv. Math. 4, 227 (1940)

1940

[3] [3]

W. F. Stinespring, Positive Functions on C* -Algebras, Proc. Am. Math. Soc. 6, 211 (1955)

1955

[4] [4]

Ozawa, Quantum measuring processes of continuous observables, J

M. Ozawa, Quantum measuring processes of continuous observables, J. Math. Phys. 25, 79 (1984)

1984

[5] [5]

DISCUSSION This work generalizes and unifies previous works relating to the thermodynamic consistency of quantum operations and measurements. In the conventional framework, thermodynamically consistent operations—interpreted as operations consuming only finite thermodynamic resources—are considered as those that are implementable via a unitary interaction...

work page 2023

[6] [6]

Purves and A

T. Purves and A. J. Short, Channels, measurements, and postselection in quantum thermodynamics, Phys. Rev. E 104, 014111 (2021)

2021

[7] [7]

Minagawa, M

S. Minagawa, M. H. Mohammady, K. Sakai, K. Kato, and F. Buscemi, Universal validity of the second law of information thermodynamics, npj Quantum Inf. 11, 18 (2025)

2025

[8] [8]

L. J. Schulman, T. Mor, and Y. Weinstein, Physical Limits of Heat-Bath Algorithmic Cooling, Phys. Rev. Lett. 94, 120501 (2005)

2005