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.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 ReportsMar 15, 20261 citation

Past of a quantum particle revisited

Berthold‐Georg Englert, Kelvin Horia, Jibo Dai +2 more

We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, ``the particle's path'' has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, ``the particle's path'' has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.

arXiv:1704.03722Physical Review AAug 21, 201753 citations

Toward a Principle of Significance

Materov

Jan 1, 20264 citations

Universal programmable devices for unambiguous discrimination

Chi Zhang, Mingsheng Ying

We discuss the problem of designing unambiguous programmable discriminators for any $n$ unknown quantum states in an $m$ -dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program registers and the data register. The program registers consist of the $n$ states, while the data register is prepared among them. The task of the discriminator is to tell us which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if $m=n$ , we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary $n$ quantum states. We also show how to use this universal discriminator to unambiguously discriminate mixed states.We discuss the problem of designing unambiguous programmable discriminators for any $n$ unknown quantum states in an $m$-dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program registers and the data register. The program registers consist of the $n$ states, while the data register is prepared among them. The task of the discriminator is to tell us which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if $m=n$, we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary $n$ quantum states. We also show how to use this universal discriminator to unambiguously discriminate mixed states.

arXiv:quant-ph/0606189Jun 22, 20060 citations

PERCEPTIONS AND REALITIES

Bruce M. Bennett, Donald D. Hoffman, Chetan Prakash

Elsevier eBooksJan 1, 19890 citations

We discuss the problem of designing unambiguous programmable discriminators for any

n

unknown quantum states in an

m

-dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program registers and the data register. The program registers consist of the

n

states, while the data register is prepared among them. The task of the discriminator is to tell us which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if

m=n

, we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary

n

quantum states. We also show how to use this universal discriminator to unambiguously discriminate mixed states.