High-fidelity multipartite entanglement creation in non-Hermitian qubits

C. G. Feyisa; C.-Y. Liu; H. H. Jen; Muhammad S. Hasan

REVIEW 2 major objections 4 minor 1 cited by

High-fidelity multipartite entanglement creation in non-Hermitian qubits

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A symmetric non-Hermitian qubit model can prepare three- and four-qubit GHZ states with near-unit fidelity in a single step.

desk verdict A clean numerical extension of prior non-Hermitian qubit work whose fidelity claims are hostage to an unreported no-jump survival probability; worth refereeing but not as-is. read the letter →

arxiv 2412.01133 v1 pith:WGPKTIAQ submitted 2024-12-02 quant-ph

C.-Y. Liu , C. G. Feyisa , Muhammad S. Hasan , H. H. Jen This is my paper · ORCID

classification quant-ph MSC 81P4081P68

keywords non-HermitianqubitsGHZstatesmultipartiteentanglementthreetangleentropysuperconductingpostselectionall-to-allcoupling

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

This paper claims that a single global step of evolution under a symmetric non-Hermitian Hamiltonian can create three- and four-qubit GHZ states, or GHZ-class states, of superconducting qubits with fidelity approaching unity. In the strong-driving regime ($\Omega=100J$), the three-qubit fidelity reaches $0.9999$ at zero decay and $0.999$ at $\gamma=6J$, while the four-qubit protocol reaches $0.998$ and $0.99$ after a local phase correction. The entanglement is certified by the three tangle for three qubits and by entanglement entropy for four qubits. If the claim is correct, this offers a one-step entangling gate that avoids sequential two-qubit gates and remains effective under modest loss rates.

What carries the argument

The load-bearing object is the renormalized postselected state $\rho(t) = |\psi(t)\rangle\langle\psi(t)| / |\langle\psi(t)|\psi(t)\rangle|$ with $|\psi(t)\rangle = e^{-i\hat H t}|\psi(0)\rangle$, where $\hat H$ is the symmetric all-to-all non-Hermitian qubit Hamiltonian with driving $\Omega$, coupling $J$, and decay $\gamma$. This renormalization conditions on the no-jump trajectory and is what turns non-unitary evolution into a candidate GHZ state; it is also the quantity on which all reported fidelities are computed. The entanglement witnesses are the three tangle $\tau$ for three qubits and the entanglement entropy $S$ for four qubits, which identify the GHZ class and the maximally entangled plateau $S \approx \log 2$.

What would settle it

At the claimed operating point ($\Omega = 100J$, $\gamma = 6J$, $Jt = \pi$), compute the no-jump survival probability $|\langle\psi(t)|\psi(t)\rangle|$ for the three- and four-qubit protocols; if it is negligible, or if an unconditioned simulation that includes quantum jumps yields a GHZ fidelity far below the reported $0.99$ values, the central claim is contradicted.

Watch

Extended reading notes

Core claim

The central discovery is that the interplay of strong driving, symmetric all-to-all couplings, and a tunable loss rate in a non-Hermitian transmon-qubit model drives the postselected no-jump state into the GHZ class. Starting from $(|f\rangle)^{\otimes 3}$ and evolving to $Jt = \pi$ with $\Omega \gg J, \gamma$, the three tangle $\tau$ approaches unity and the fidelity to the GHZ state exceeds $0.999$, even at $\gamma = 6J$. For four qubits, the same evolution produces a state that, up to a single-qubit $Z(3\pi/4)$ rotation, has fidelity $\approx 0.998$ at $\gamma = 0$ and $\approx 0.99$ at $\gamma = 6J$. In the strong-coupling regime ($J \gg \Omega, \gamma$) with spin-coherent initial states, GHZ-class states appear at odd multiples of $Jt = \pi/2$ and remain robust for small $\gamma$. The paper concludes that non-Hermitian qubit systems can host genuine maximal multipartite entanglement in a one-step protocol.

Load-bearing premise

The near-unit fidelities are computed on the branch of the dynamics where no loss event happens, and the paper never reports the probability of actually staying on that branch, so the state may not be produced with a useful probability in practice.

Editorial extensions

If this is right

In the strong-driving limit, a single global evolution step prepares a three-qubit GHZ-class state with fidelity $0.9999$ at $\gamma = 0$ and $0.999$ at $\gamma = 6J$ when $Jt = \pi$.
The same protocol prepares a four-qubit GHZ state up to a local $Z(3\pi/4)$ rotation, with fidelity $0.998$ at $\gamma = 0$ and $0.99$ at $\gamma = 6J$.
GHZ-class generation stays robust for decay rates up to $\gamma = 6J$ when the drive is strong, and moderate drives still show revivals of the three tangle at larger $\gamma$.
These one-step schemes avoid sequences of two-qubit entangling gates, reducing the time and circuit complexity needed for multipartite entanglement creation.
The strong-coupling regime with spin-coherent initial states offers an alternative route, producing GHZ-class states at odd multiples of $Jt = \pi/2$.

Reading between the lines

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

The missing success probability is the key practical quantity to add: because all quoted fidelities are conditional on no jump, one should report $|\langle\psi(t)|\psi(t)\rangle|$ and simulate the unconditioned master equation before claiming a usable source of GHZ states.
A natural extension is to $N > 4$ qubits: the symmetric all-to-all dynamics likely generalizes, but the no-jump probability will typically fall exponentially with $N$ and with $\gamma t$, so the fidelity-versus-success-rate trade-off should be quantified.
The revival of $\tau$ at moderate $\Omega$ suggests an optimization landscape in which one can choose $(\Omega, \gamma, J)$ to balance fidelity, speed, and resource cost, a direction the authors mention but do not fully map.
Because the model assumes the decay from $|f\rangle$ is negligible relative to that from $|e\rangle$, including a finite $|f\rangle$ loss channel could shift the optimal times and fidelities; testing this would constrain the validity of the two-level reduction.

Share X Bluesky LinkedIn Reddit HN

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

Colleague,

You should know two things about arXiv:2412.01133. First, it is a straightforward numerical extension of the authors' earlier work on non-Hermitian qubits: same Hamiltonian, same entanglement measures, now run for three and four qubits in the strong-driving and strong all-to-all coupling regimes. Second, all quoted fidelities (F ≈ 0.999, etc.) are conditional on the no-jump branch of the quantum trajectory, but the probability of that branch is never reported. That is the paper's real soft spot.

What the paper does well: the numerics are simple and almost certainly correct for the stated postselected evolution. The three-tangle plots in Figs. 2 and 3 show robust maxima near unity, and the authors are transparent about using the renormalized state of Eq. (1). The observation that strong driving sustains GHZ-class fidelity over a wide range of decay rates is a genuine, if modest, addition. The same holds for the strong-coupling regime with spin-coherent initial states, though the choice of phase phi needs a scan to be fully convincing.

The main problem is the missing no-jump probability. The paper computes everything from e^{-iHt}|psi0>, normalized, and calls that the generated state. But that state is conditioned on zero jumps into the loss channel. The actual probability of that branch, P_succ(t) = , is never plotted or tabulated. At gamma = 6J and Jt = pi, gamma t ≈ 18.8, and with half the population in the decaying |e> state, P_succ is likely exponentially small. If so, the abstract's claim that high-fidelity states 'can be created' is not supported as a practical protocol. The paper also never simulates unconditioned trajectories, so it gives no evidence about the average output state. This is missing support, not an internal contradiction, and it can be fixed by reporting P_succ and, ideally, the unconditioned dynamics.

A secondary issue: for four qubits, the paper relies on single-qubit entanglement entropy S ≈ log 2 as evidence of GHZ-class entanglement. That is not a multipartite witness; many non-GHZ states share this entropy. They also mention one local Z-rotation to match the GHZ state, but a fixed phase gate at one time point does not replace a parameter scan.

Who is this for? People working on non-Hermitian quantum engineering who care about postselected entanglement generation. The paper deserves a serious referee: the main numbers are checkable, the omission is addressable, and the model sits in a growing literature. My recommendation: send it to review with a request to report P_succ and to either add a multipartite witness for four qubits or soften the strength of the claims.

Referee Report

2 major / 4 minor

Summary. The manuscript studies a symmetric all-to-all coupled model of non-Hermitian superconducting qubits, with the Hamiltonian introduced in Sec. II, and analyzes the postselected no-jump evolution of pure states. For three qubits it computes the three-tangle dynamics and GHZ fidelity in the strong-driving (Ω ≫ J, γ) and strong-coupling (J ≫ Ω, γ) regimes; for four qubits it plots single-qubit entanglement entropy and reports GHZ fidelity at one operating time. The main quantitative claims are F ≈ 0.9999 and 0.999 for the three-qubit GHZ state at γ = 0 and γ = 6J with Ω = 100J at Jt = π (Sec. III.A), and F ≈ 0.998 and 0.99 for the four-qubit GHZ state at γ = 0 and γ = 6J with Ω = 100J at Jt = π (Sec. IV), up to a single-qubit phase gate. All of these fidelities are evaluated on the renormalized state defined in Eq. (1), i.e. on the no-jump branch of the non-Hermitian evolution.

Significance. If the no-jump branch occurs with non-negligible probability, the paper would demonstrate a simple one-step protocol producing high-fidelity GHZ and GHZ-class states in a dissipative circuit-QED platform, with no parameter fitting: the Hamiltonian is explicit, the target-state fidelity is computed directly, and the claimed robustness to γ is checkable from the displayed dynamics. However, because the central output is conditional, the practical significance hinges on a quantity the paper never reports: the success probability of the postselected branch. The manuscript therefore currently establishes a conditional entanglement-generation claim, not a practical generation scheme. The strength of the paper is that the numerics are transparent and the measures (three-tangle, entropy, fidelity) are standard; the weakness is the unquantified role of postselection and the absence of trajectory-averaged or unconditional results.

major comments (2)

[II, Eq. (1); III.A; IV] All fidelity values quoted in the abstract and in Sections III and IV are computed from the postselected, renormalized state ρ(t)=|ψ(t)⟩⟨ψ(t)|/|⟨ψ(t)|ψ(t)⟩| defined in Eq. (1). This state conditions on the absence of any quantum jump into the loss channel, yet the paper never reports the no-jump survival probability P_succ(t)=⟨ψ(t)|ψ(t)⟩, nor does it simulate unconditioned quantum trajectories or the Lindblad master equation. At the operating point γ=6J, Jt=π (Sec. III.A), the integrated loss γt is about 18.8, so P_succ could be exponentially small; if so, the high conditional fidelity does not imply that a high-fidelity GHZ state is created in a useful fraction of runs. The central practical claim in the abstract therefore lacks load-bearing support. The authors should report P_succ at the quoted operating points, show its time dependence, and provide either the unconditioned average-state fidelity or an explicit heralding model for the no-jump branch.
[III.B, Fig. 3] The strong-coupling protocol is presented as one of the two central routes, but the manuscript reports no fidelity number in this regime and no quantitative check of the stated insensitivity to the initial phase φ. The initial spin-coherent state is chosen with φ ≈ 0.288π, and the text asserts that different φ values show similar dynamics, but no scan or supporting data is shown. If the high-fidelity GHZ-class generation depends sensitively on φ, then φ is effectively a tuned parameter rather than an arbitrary phase. Please provide a φ-dependence plot for τ and for the target-state fidelity, and report the fidelity achieved at the operating point of Fig. 3.

minor comments (4)

[IV (title)] The section title 'FOUR QUBTIS' should be corrected to 'FOUR QUBITS'.
[IV, Fig. 4] The sentence 'The system generates a particular GHZ class state during the period when S reaches around log 2' is too strong: a single-qubit entanglement entropy of log 2 is necessary but not sufficient for a four-qubit GHZ-class state. The fidelity F reported at Jt=π is the appropriate witness and should be presented as the primary evidence; the entropy plateaus should be described as an indicator only.
[III.B] The statement that the strong-coupling regime 'corresponds to the PT symmetric phase as it yields real eigenvalues' is not supported by any spectral calculation in the manuscript; please add a brief derivation or soften the claim.
[IV] The four-qubit fidelity is quoted only in the text after applying Z(3π/4) to one qubit; please state explicitly that this is a local unitary and give the unrotated state coefficients or a distance measure so the result is reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central fidelities are direct Schrödinger-evolution results compared against fixed GHZ targets, with no parameter fitted to those targets and no load-bearing self-citation chain.

full rationale

The quantitative claims are obtained by evolving the model Hamiltonian of Eq. (1) through Eq. (2), then evaluating the standard three-tangle τ from Eq. (5) and the fidelity F from Eq. (9) against the fixed GHZ targets |eee⟩+|fff⟩ over √2 and |eeee⟩+|ffff⟩ over √2. No parameter is fitted to those targets: Ω, γ, J, and the initial-state phase ϕ are chosen before the evolution, and the paper states that 'different ϕ’s show similar time dynamics and properties in our plots,' so the representative ϕ is not a contrived fit. The only post-evolution adjustment in Section IV is a single-qubit Z rotation, which is LOCC and does not change the entanglement class; applying it before computing fidelity is therefore not circular. The self-citations ([28], [29], [31]) provide the non-Hermitian model form and background, but the load-bearing result is the direct numerical evolution reported here, not an imported theorem or uniqueness claim. The main weakness is a missing-support issue rather than circularity: Eq. (1) defines the postselected, renormalized state, and the paper never reports the no-jump probability |⟨ψ(t)|ψ(t)⟩| or simulates unconditioned trajectories, so the practical creation probability at γ=6J is unquantified. That gap does not make the fidelity computation equal to its input by construction, so it does not raise the circularity score.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The model uses only the non-Hermitian Hamiltonian imported from cited prior work; no new particles, forces, or dimensions are introduced. The main ledger entries are the postselection rule, the effective two-level reduction, and the symmetric parameter assumption. The only hand-chosen numerical input listed is the representative initial phase phi.

free parameters (1)

Initial spin-coherent phase phi = approximately 0.288 pi
Hand-chosen representative value for the strong-coupling initial state in Fig. 3; the text says other phi behave similarly but no scan is shown, so insensitivity is asserted rather than demonstrated.

assumptions (4)

domain assumption The no-jump postselected state rho(t) = |psi(t)><psi(t)| / <psi(t)|psi(t)> is the quantity whose fidelity is reported.
Invoked in Eq. (1) and used for all tangle, entropy, and fidelity calculations; it assumes the experiment keeps only runs with no quantum jump.
domain assumption A dominant |e> to |g> decay reduces each three-level transmon to an effective two-level non-Hermitian qubit with states |e>, |f>, and no dynamical role for |g>.
Assumed in Section II and Fig. 1 to justify the non-Hermitian Hamiltonian.
domain assumption The qubits are symmetric with J_jk = J, Omega_j = Omega, gamma_j = gamma, and resonant drives Delta_j = 0.
Imposed in Section II; this symmetry underlies the uniform GHZ-target dynamics and is not derived from a specific experimental platform.
standard math The standard pure-state three-tangle formula tau = 4|d1 - 2d2 + 4d3| applies to the normalized postselected amplitudes.
Used in Sections II and III A to certify GHZ-class entanglement for three qubits.

how reviews work

0 comments

Cite this review

Pith. "Pith review of High-fidelity multipartite entanglement creation in non-Hermitian qubits." pith.science (2026). https://pith.science/paper/WGPKTIAQ

@misc{pith2026241201133,
  author       = {Pith},
  title        = {Pith review of: High-fidelity multipartite entanglement creation in non-Hermitian qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WGPKTIAQ}},
  note         = {Machine review of arXiv:2412.01133}
}

read the original abstract

Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the PT (parity and time) symmetry phase transition, where an enhanced spectral sensitivity arises and leads to novel quantum engineering. Here we theoretically study the multipartite entanglement properties in non-Hermitian superconducting qubits, where high-fidelity entangled states can be created under strong driving fields or strong couplings among the qubits. Under an interplay between driving fields, couplings, and non-Hermiticity, we focus on generations of GHZ states or GHZ classes in three and four qubits with all-to-all couplings, which allows a fidelity approaching unity when relatively low non-Hermitian decay rates are considered. This presents an ultimate capability of non-Hermitian qubits to host a genuine and maximal multipartite entanglement. Our results can shed light on novel quantum engineering of multipartite entanglement generations in non-Hermitian qubit systems.

Figures

Figures reproduced from arXiv: 2412.01133 by the authors.

**Figure 2.** FIG. 2. Three tangle dynamics in the strong driving regime. We demonstrate three examples of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Three tangle dynamics under the strong coupling regime from an initial spin coherent state [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Two-level control over quantum state creation via entangled equal-probability state
quant-ph 2025-02 conditional novelty 6.0 of 10

A two-level ancilla-control protocol where phase constraints on an equal-probability auxiliary state simultaneously set its bipartite concurrence and the number of conditional unitaries that a second controller can sw...

Reference graph

Works this paper leans on

48 extracted references · 32 canonical work pages · cited by 1 Pith paper

[1]

Ashida, Z

Y . Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys.69, 249 (2020)

2020
[2]

The single-qubit phase gate Z (ϕ) [46] can be denoted as Z (ϕ) ≡ eiϕ 0 0 1

The generated state |ψ (t)⟩ indeed resembles the |ψGHz⟩ only up to single-qubit rotations, which is Z 3π 4 ⊗ I ⊗ I ⊗ I)|ψ (t)⟩ ≈ |ψGHz⟩ with fidelity F ≈ 0.998 and 0.99 for γ = 0 and 6J, respectively. The single-qubit phase gate Z (ϕ) [46] can be denoted as Z (ϕ) ≡ eiϕ 0 0 1 . (10) V . CONCLUSION AND DISCUSSION In conclusion, we theoretically explore the ...

work page
[3]

E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021)

2021
[4]

Wiersig, Enhancing the Sensitivity of Frequency and Energy Splitting Detection by Using Exceptional Points: Application to Micro- cavity Sensors for Single-Particle Detection, Phys

J. Wiersig, Enhancing the Sensitivity of Frequency and Energy Splitting Detection by Using Exceptional Points: Application to Micro- cavity Sensors for Single-Particle Detection, Phys. Rev. Lett.112, 203901 (2014)

work page 2014
[5]

Hodaei, A

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature 548, 187 (2017)

2017
[6]

Doppler, A

J. Doppler, A. A. Mailybaev, J. B ¨ohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, Dynamically encircling an exceptional point for asymmetric mode switching, Nature 537, 76 (2016)

work page 2016
[7]

Y . Choi, C. Hahn, J. W. Yoon, S. H. Song, and P. Berini, Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points, Nat. Commun. 8, 14154 (2017)

work page 2017
[8]

X. L. Zhang, S. Wang, B. Hou, and C. T. Chan, Dynamically Encircling Exceptional Points: In Situ Control of Encircling Loops and the Role of the Starting Point, Phys. Rev. X 8, 021066 (2018)

work page 2018

Show all 48 references

[9]

M. A. Miri and A. Al `u, Exceptional points in optics and photonics, Science 363, eaar7709 (2019)

2019
[10]

Ozawa, H

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys.91, 015006 (2019)

2019
[11]

Abbasi, W

M. Abbasi, W. Chen, M. Naghiloo, Y . N. Joglekar, and K. W. Murch, Topological Quantum State Control through Exceptional-Point Proximity, Phys. Rev. Lett.128, 160401 (2022)

2022
[12]

Minganti, A

F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: the effects of quantum jumps, Phys. Rev. A 100, 062131 (2019)

2019
[13]

C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rep. Prog. Phys. 70, 947 (2007)

2007
[14]

El-Ganainy, K

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018)

2018
[15]

K.¨Ozdemir, S

S ¸. K.¨Ozdemir, S. Rotter, F. Nori, and L. Yang, Parity-time symmetry and exceptional points in photonics, Nat. Mater.18, 783 (2019)

2019
[16]

J Li, A. K. Harter, J. Liu, L. de Melo, Y . N. Joglekar, and L. Luo, Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms, Nat. Commun. 10, 855 (2019)

2019
[17]

T. E. Lee, Anomalous Edge State in a Non-Hermitian Lattice, Phys. Rev. Lett. 116, 133903 (2016)

2016
[18]

Yao and Z

S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

2018
[19]

V . M. Martinez Alvarez, J. E. Barrios Vargas, and L.E. F. Foa Torres, Non-Hermitian robust edge states in one dimension: anomalous localization and eigenspace condensation at exceptional points, Phys. Rev. B 97, 121401(R) (2018)

2018
[20]

F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Biorthogonal bulk boundary correspondence in non-hermitian systems, Phys. Rev. Lett. 121, 026808 (2018)

2018
[21]

C. H. Lee and R. Thomale, Anatomy of skin modes and topology in non-Hermitian systems, Phys. Rev. B 99, 201103(R) (2019)

2019
[22]

D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non-hermitian boundary modes and topology, Phys. Rev. Lett. 124, 056802 (2020)

2020
[23]

Okuma, K

N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological origin of non-hermitian skin effects, Phys. Rev. Lett.124, 086801 (2020)

2020
[24]

Zhang, Z

K. Zhang, Z. Yang, and C. Fang, Correspondence between winding numbers and skin modes in non-hermitian systems, Phys. Rev. Lett. 125, 126402 (2020)

2020
[25]

Zhang, Z

K. Zhang, Z. Yang, and C. Fang, Universal non-Hermitian skin effect in two and higher dimensions. Nat. Commun. 13, 2496 (2022)

2022
[26]

Wang, J.-S

Y .-C. Wang, J.-S. You, and H. H. Jen, A non-Hermitian optical atomic mirror, Nat. Commun.13, 4598 (2022)

2022
[27]

H. Wang, J. Zhong, and S. Fan, Non-Hermitian photonic band winding and skin effects: a tutorial, Advances in Optics and Photonics 16, 659 (2024)

2024
[28]

H. H. Jen, Photon-mediated dipole-dipole interactions as a resource for quantum science and technology in cold atoms, arXiv:2410.20665 (2024)

2024 arXiv
[29]

Z.-Z. Li, W. Chen, M. Abbasi, K. W. Murch, and K. B.Whaley, Speeding Up Entanglement Generation by Proximity to Higher-Order Exceptional Points, Phys. Rev. Lett. 131, 100202 (2023)

2023
[30]

C. G. Feyisa, J.-S. You, H.-Y . Ku, and H. H. Jen, Accelerating multipartite entanglement generation in non-hermitian superconducting qubits, arXiv:2409.03414 (2024)

2024 arXiv
[31]

Zhang, Z.-T

Y .-X. Zhang, Z.-T. Zhang, X.-Z. Wei, B.-L. Liang,F. Mei, and Z.-S. Yang, Entanglement dynamics of two non-hermitian qubits, J. of Phys. B 57, 085501 (2024)

2024
[32]

C. G. Feyisa, C.-Y . Liu, M. S. Hasan, J.-S. You, H.-Y . Ku, H. H. Jen, Robustness of tripartite entangled states in passivePT -symmetric qubits, arXiv:2411.17457 (2024)

2024 arXiv
[33]

D. M. Greenberger, M. A. Horne, and A. Zeilinger, Bell’s Theorem, Quantum Theory and Conceptions of the Universe, 69–72 (Kluwer Academic, 1989)

1989
[34]

Neeley, R

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero,M. Mariantoni, A. O’connell, D. Sank, H. Wang, M. Weides, J. Wenner,et al., Nature 467, 570 (2010). 7

2010
[35]

Wallraff, D

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.- S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature 431, 162 (2004)

2004
[36]

Blais, R.-S

A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation, Phys. Rev. A 69, 062320 (2004)

2004
[37]

DiCarlo, M

L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Preparation and measurement of three-qubit entanglement in a superconducting circuit, Nature 467, 574 (2010)

2010
[38]

T. Roy, S. Hazra, S. Kundu, M. Chand, M. P. Patankar,and R. Vijay, Programmable superconducting processor with native three-qubit gates, Phys. Rev. Applied 14, 014072 (2020)

2020
[39]

C. Zhou, P. Lu, M. Praquin, T.-C. Chien, R. Kaufman,X. Cao, M. Xia, R. S. Mong, W. Pfaff, D. Pekker, et al. , Realizing all-to-all couplings among detachable quantum modules using a microwave quantum state router, npj Quantum Information 9, 54 (2023)

2023
[40]

X. Wu, H. Yan, G. Andersson, A. Anferov, M.-H. Chou, C. R. Conner, J. Grebel, Y . J. Joshi, S. Li, J. M. Miller,et al., Modular Quantum Processor with an All-to-All Reconfigurable Router, Phys. Rev. X14, 041030 (2024)

2024
[41]

Coffman, J

V . Coffman, J. Kundu, and W. K. Wootters, Distributed entanglement, Phys. Rev. A61, 052306 (2000)

2000
[42]

Naghiloo, M

M. Naghiloo, M. Abbasi, Y . N. Joglekar, and K. Murch, Quantum state tomography across the exceptional point in a single dissipative qubit, Nat. Phys. 15, 1232 (2019)

2019
[43]

Horodecki, P

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev.Mod. Phys. 81, 865 (2009)

2009
[44]

Islam, R

R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin,M. Rispoli, and M. Greiner, Measuring entanglement entropy in a quantum many- body system, Nature 528, 77 (2015)

2015
[45]

D ¨ur, G

W. D ¨ur, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A62,062314 (2000)

2000
[46]

W. K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Phys. Rev. Lett.80, 2245 (1998)

1998
[47]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge university press, Cambridge, 2001)

2001
[48]

X. Gu, J. Fern\’andez-Pend\’as, P. Vikst\aa{}l, T. Abad, C. Warren, A. Bengtsson, G. Tancredi, V . Shumeiko, J. Bylander, G. Johansson, and A. F. Kockum, Fast Multiqubit Gates through Simultaneous Two-Qubit Gates, PRX Quantum2, 040348 (2021)

2021

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Ashida, Z

Y . Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys.69, 249 (2020)

2020

[2] [2]

The single-qubit phase gate Z (ϕ) [46] can be denoted as Z (ϕ) ≡ eiϕ 0 0 1

The generated state |ψ (t)⟩ indeed resembles the |ψGHz⟩ only up to single-qubit rotations, which is Z 3π 4 ⊗ I ⊗ I ⊗ I)|ψ (t)⟩ ≈ |ψGHz⟩ with fidelity F ≈ 0.998 and 0.99 for γ = 0 and 6J, respectively. The single-qubit phase gate Z (ϕ) [46] can be denoted as Z (ϕ) ≡ eiϕ 0 0 1 . (10) V . CONCLUSION AND DISCUSSION In conclusion, we theoretically explore the ...

work page

[3] [3]

E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021)

2021

[4] [4]

Wiersig, Enhancing the Sensitivity of Frequency and Energy Splitting Detection by Using Exceptional Points: Application to Micro- cavity Sensors for Single-Particle Detection, Phys

J. Wiersig, Enhancing the Sensitivity of Frequency and Energy Splitting Detection by Using Exceptional Points: Application to Micro- cavity Sensors for Single-Particle Detection, Phys. Rev. Lett.112, 203901 (2014)

work page 2014

[5] [5]

Hodaei, A

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature 548, 187 (2017)

2017

[6] [6]

Doppler, A

J. Doppler, A. A. Mailybaev, J. B ¨ohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, Dynamically encircling an exceptional point for asymmetric mode switching, Nature 537, 76 (2016)

work page 2016

[7] [7]

Y . Choi, C. Hahn, J. W. Yoon, S. H. Song, and P. Berini, Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points, Nat. Commun. 8, 14154 (2017)

work page 2017

[8] [8]

X. L. Zhang, S. Wang, B. Hou, and C. T. Chan, Dynamically Encircling Exceptional Points: In Situ Control of Encircling Loops and the Role of the Starting Point, Phys. Rev. X 8, 021066 (2018)

work page 2018