Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2209.02481 · Physical Review A

Quantum state discrimination in a PT -symmetric system

Dong‐Xu Chen, Yu Zhang, Jun‐Long Zhao, Qi‐Cheng Wu, Yu-Liang Fang, Chui‐Ping Yang, Franco Nori

Published Aug 30, 2022• 14 citations
arXivHTMLPDF

Abstract

Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-($\mathcal{PT}$-)symmetric non-Hermitian quantum systems exhibit novel phenomena and have attracted considerable attention. Here, we experimentally demonstrate QSD in a $\mathcal{PT}$-symmetric system (i.e., $\mathcal{PT}$-symmetric QSD), by having quantum states evolve under a $\mathcal{PT}$-symmetric Hamiltonian in a lossy linear optical setup. We observe that two initially nonorthogonal states can rapidly evolve into orthogonal states and the required evolution time can even be vanishing provided the matrix elements of the Hamiltonian become sufficiently large. We also observe that the cost of such a discrimination is a dissipation of quantum states into the environment. Furthermore, by comparing $\mathcal{PT}$-symmetric QSD with optimal strategies in Hermitian systems, we find that at the critical value, $\mathcal{PT}$-symmetric QSD is equivalent to the optimal unambiguous state discrimination in Hermitian systems. We also extend the $\mathcal{PT}$-symmetric QSD to the case of discriminating three nonorthogonal states. The QSD in a $\mathcal{PT}$-symmetric system opens a new door for quantum state discrimination, which has important applications in quantum computing, quantum cryptography, and quantum communication.

DOI
10.1103/physreva.106.022438

Related papers

A Guiding Principle for Quantum State Discrimination in the Real-Spectrum Phase of P-Pseudo-Hermitian Systems

Qinliang Dong, Xue-Er Gao, Zhihang Liu +3 more

Quantum state discrimination (QSD) is a fundamental task in quantum information processing, improving the computation efficiency and communication security. Non-Hermitian (NH) PT-symmetric systems were found to be able to discriminate two quantum states better than the Hermitian strategy. In this work, we propose a QSD approach based on P-pseudo-Hermitian systems with real spectra. We theoretically prove the feasibility of realizing QSD in the real-spectrum phase of a P-pseudo-Hermitian system, i.e., two arbitrary non-orthogonal quantum states can be discriminated by a suitable P-pseudo-Hermitian Hamiltonian. In detail, we decide the minimal angular separation between two non-orthogonal quantum states for a fixed P-pseudo-Hermitian Hamiltonian, and we find the orthogonal evolution time is able to approach zero under suitable conditions, while both the trace distance and the quantum relative entropy are employed to judge their orthogonality. We give a criterion to choose the parameters of a P-pseudo-Hermitian Hamiltonian that evolves the two initial orthogonal states faster than a fixed arbitrary PT-symmetric one with an identical energy difference. Our work expands the NH family for QSD, and can be used to explore real quantum systems in the future.

Entropy•Aug 6, 2025•6 citations

Non-Hermitian quantum state discrimination and information flow

QINLIANG Dong, Zhihang Liu, Chao Zheng

As a fundamental and challenging problem in quantum information processing, quantum state discrimination (QSD) has recently been revisited from the perspective of non-Hermitian (NH) physics. The existing work about QSD in NH systems is mostly limited to PT-symmetric or pseudo-Hermitian systems with real spectra, while generic NH Hamiltonians possess complex spectra. To explore the underlying physics of quantum state discrimination in NH systems, we first demonstrate that the unambiguous discrimination of non-orthogonal quantum states can be realized with P-pseudo-Hermitian and PT-symmetric Hamiltonians in the broken phase and the required evolution time can be arbitrarily small. We further extend the regime to generic non-Hermitian Hamiltonians and demonstrate the feasibility of unambiguous discrimination. Under the same energy constraint, we establish the criteria for constructing P-pseudo-Hermitian Hamiltonians that enable unambiguous discrimination of quantum states with smaller angular separation or within shorter evolution time than any fixed PT-symmetric system. Furthermore, we also discuss the potential impact of exceptional points (EPs) on QSD. Our results suggest that the non-orthogonal eigenstates of NH Hamiltonians, rather than PT symmetry or pseudo-Hermitian symmetry, are fundamental to unambiguous discrimination and information flow in NH systems.

Scientific Reports•Mar 15, 2026•1 citation

Unambiguous Quantum State Discrimination in a PT$\mathcal {PT}$‐Symmetric System of a Single Trapped Ion

Chenhao Zhu, Tingting Shi, Liangyu Ding +3 more

Abstract An unambiguous quantum state discrimination of two qubit states is experimentally demonstrated under a non‐Hermitian Hamiltonian with parity‐time‐reversal () symmetry in a single trapped 40 Ca + ion. It is shown that any two non‐orthogonal states can become orthogonal subjected to time evolution of a ‐symmetric Hamiltonian in both the ‐symmetry preserving and broken regimes, thus can be discriminated unambiguously. For a given pair of candidate states, it is shown that the parameters of the Hamiltonian must be confined in a proper range, within which there exists an optimal choice to realize quantum brachistochrone for the fastest orthogonalization. Besides, a clear geometric picture and some analytic results are provided to understand the main conclusions. This work shows a promising application of non‐Hermitian physics in quantum information processing.

Advanced Science•Aug 24, 2025•3 citations

Recovery of contextuality based on mirror-like state discrimination in PT- and anti-PT-symmetric systems

Xuan Fan, Xiao, Ya, Yongjian Gu

In the past decades, researches on parity-time (PT) and anti-parity-time(APT) systems have garnered unprecedented attention, showcasing their various intriguing characteristics and promising potentiality in extending canonical Hermitian quantum mechanics. However, despite significant endeavors devoted to this new field of physics, non-Hermitian dynamics of contextuality still remains an uncharted region, either in PT-symmetry or APT-symmetry systems. Since contextuality has also been proven to be the core resource for quantum state discrimination (QSD) tasks, here we systematically investigate the novel performance of contextuality through QSD in both systems, taking mirror-symmetric three-state minimum error discrimination (MED) and maximum confidence discrimination (MCD) scenarios as two examples. The time evolution of contextuality in two scenarios and eight regimes (four regimes for each scenario) are comprehensively compared and analyzed, with the difference of initial states also considered. In the symmetry-unbroken regimes, our simulation shows periodic oscillations of contextuality for both MED and MCD scenarios, the period of which is state-independent but related to non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of contextuality exceeding its initial value in PT system, which is only existent for MCD in APT system. In the symmetry-broken regimes, the success probabilities of both scenarios start from a prompt decay at first, ending up with a stable value which is constantly 1/3. Non-triviality is found only for MCD scenario in PT system, where the recovered contextuality exceeds its initial value.

arXiv:2403.08076•Mar 12, 2024•0 citations

Experimental scheme for unambiguous discrimination of linearly independent symmetric states

O. Jiménez, X. Sánchez-Lozano, Enrique B. Inostroza +2 more

We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among $N$ linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.

arXiv:0705.3813•Physical Review A•Dec 11, 2007•19 citations

PT -symmetric quantum state discrimination

Carl M. Bender, Dorje C. Brody, João Luiz Caldeira +3 more

The objective of this paper is to explain and elucidate the formalism of PT quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ(1)> or |ψ(2)>. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of PT quantum mechanics and the approach is based on the fact that a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states |ψ(1)> and |ψ(2)> are orthogonal. Using PT quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability p.

arXiv:1011.1871•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Mar 19, 2013•39 citations
Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-(PT\mathcal{PT}PT-)symmetric non-Hermitian quantum systems exhibit novel phenomena and have attracted considerable attention. Here, we experimentally demonstrate QSD in a PT\mathcal{PT}PT-symmetric system (i.e., PT\mathcal{PT}PT-symmetric QSD), by having quantum states evolve under a PT\mathcal{PT}PT-symmetric Hamiltonian in a lossy linear optical setup. We observe that two initially nonorthogonal states can rapidly evolve into orthogonal states and the required evolution time can even be vanishing provided the matrix elements of the Hamiltonian become sufficiently large. We also observe that the cost of such a discrimination is a dissipation of quantum states into the environment. Furthermore, by comparing PT\mathcal{PT}PT-symmetric QSD with optimal strategies in Hermitian systems, we find that at the critical value, PT\mathcal{PT}PT-symmetric QSD is equivalent to the optimal unambiguous state discrimination in Hermitian systems. We also extend the PT\mathcal{PT}PT-symmetric QSD to the case of discriminating three nonorthogonal states. The QSD in a PT\mathcal{PT}PT-symmetric system opens a new door for quantum state discrimination, which has important applications in quantum computing, quantum cryptography, and quantum communication.
Quantum state discrimination (QSD) is a fundamental task in quantum information processing, improving the computation efficiency and communication security. Non-Hermitian (NH) PT-symmetric systems were found to be able to discriminate two quantum states better than the Hermitian strategy. In this work, we propose a QSD approach based on P-pseudo-Hermitian systems with real spectra. We theoretically prove the feasibility of realizing QSD in the real-spectrum phase of a P-pseudo-Hermitian system, i.e., two arbitrary non-orthogonal quantum states can be discriminated by a suitable P-pseudo-Hermitian Hamiltonian. In detail, we decide the minimal angular separation between two non-orthogonal quantum states for a fixed P-pseudo-Hermitian Hamiltonian, and we find the orthogonal evolution time is able to approach zero under suitable conditions, while both the trace distance and the quantum relative entropy are employed to judge their orthogonality. We give a criterion to choose the parameters of a P-pseudo-Hermitian Hamiltonian that evolves the two initial orthogonal states faster than a fixed arbitrary PT-symmetric one with an identical energy difference. Our work expands the NH family for QSD, and can be used to explore real quantum systems in the future.
As a fundamental and challenging problem in quantum information processing, quantum state discrimination (QSD) has recently been revisited from the perspective of non-Hermitian (NH) physics. The existing work about QSD in NH systems is mostly limited to PT-symmetric or pseudo-Hermitian systems with real spectra, while generic NH Hamiltonians possess complex spectra. To explore the underlying physics of quantum state discrimination in NH systems, we first demonstrate that the unambiguous discrimination of non-orthogonal quantum states can be realized with P-pseudo-Hermitian and PT-symmetric Hamiltonians in the broken phase and the required evolution time can be arbitrarily small. We further extend the regime to generic non-Hermitian Hamiltonians and demonstrate the feasibility of unambiguous discrimination. Under the same energy constraint, we establish the criteria for constructing P-pseudo-Hermitian Hamiltonians that enable unambiguous discrimination of quantum states with smaller angular separation or within shorter evolution time than any fixed PT-symmetric system. Furthermore, we also discuss the potential impact of exceptional points (EPs) on QSD. Our results suggest that the non-orthogonal eigenstates of NH Hamiltonians, rather than PT symmetry or pseudo-Hermitian symmetry, are fundamental to unambiguous discrimination and information flow in NH systems.
Unambiguous Quantum State Discrimination in a PTPT\mathcal {PT}PT‐Symmetric System of a Single Trapped Ion
Abstract An unambiguous quantum state discrimination of two qubit states is experimentally demonstrated under a non‐Hermitian Hamiltonian with parity‐time‐reversal () symmetry in a single trapped 40 Ca + ion. It is shown that any two non‐orthogonal states can become orthogonal subjected to time evolution of a ‐symmetric Hamiltonian in both the ‐symmetry preserving and broken regimes, thus can be discriminated unambiguously. For a given pair of candidate states, it is shown that the parameters of the Hamiltonian must be confined in a proper range, within which there exists an optimal choice to realize quantum brachistochrone for the fastest orthogonalization. Besides, a clear geometric picture and some analytic results are provided to understand the main conclusions. This work shows a promising application of non‐Hermitian physics in quantum information processing.
In the past decades, researches on parity-time (PT) and anti-parity-time(APT) systems have garnered unprecedented attention, showcasing their various intriguing characteristics and promising potentiality in extending canonical Hermitian quantum mechanics. However, despite significant endeavors devoted to this new field of physics, non-Hermitian dynamics of contextuality still remains an uncharted region, either in PT-symmetry or APT-symmetry systems. Since contextuality has also been proven to be the core resource for quantum state discrimination (QSD) tasks, here we systematically investigate the novel performance of contextuality through QSD in both systems, taking mirror-symmetric three-state minimum error discrimination (MED) and maximum confidence discrimination (MCD) scenarios as two examples. The time evolution of contextuality in two scenarios and eight regimes (four regimes for each scenario) are comprehensively compared and analyzed, with the difference of initial states also considered. In the symmetry-unbroken regimes, our simulation shows periodic oscillations of contextuality for both MED and MCD scenarios, the period of which is state-independent but related to non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of contextuality exceeding its initial value in PT system, which is only existent for MCD in APT system. In the symmetry-broken regimes, the success probabilities of both scenarios start from a prompt decay at first, ending up with a stable value which is constantly 1/3. Non-triviality is found only for MCD scenario in PT system, where the recovered contextuality exceeds its initial value.
We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among NNN linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.
The objective of this paper is to explain and elucidate the formalism of PT quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ(1)> or |ψ(2)>. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of PT quantum mechanics and the approach is based on the fact that a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states |ψ(1)> and |ψ(2)> are orthogonal. Using PT quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability p.