Conserved quantities in parity-time symmetric systems

Bian, Zhihao; Liu, Xiao; Wang, Kunkun; Zhan, Xiang; Onanga, Franck Assogba; Ruzicka, Frantisek; Wu, Yi; Joglekar, Yogesh N.; Xue, Peng

doi:10.1103/physrevresearch.2.022039

Cited by 43 publications

(32 citation statements)

References 37 publications

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“…A class of Hamiltonians with PT-symmetry, which commute with the joint operation parity P and time-reversal operator T , was found to be able to keep the eigenvalues of H real in the exact PT phase [ 23 ]. Since then, PT quantum mechanics has been extensively investigated theoretically [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 ] and experimentally [ 12 , 13 , 14 , 45 , 46 , 47 , 48 ]. In fact, P -pseudo-Hermiticity was pointed out to be a sufficient and necessary condition to keep the spectrum of a non-Hermitian Hamiltonian purely real [ 49 , 50 , 51 ], and both the theory and applications are developed further [ 52 , 53 , 54 , 55 , 56 , 57 ].…”

Section: Introductionmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

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Section: Introductionmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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“…However, the EP degeneracies also occur in dissipative systems with mode-selective losses. Such passive PT -symmetric systems have been realized in the quantum domain with lossy, single-photons [31][32][33][34][35][36][37][38], ultracold atoms [39], and a superconducting transmon [40]. These realizations are limited to effective twodimensional Hamiltonians with second-order EPs, and their quantum information studies are confined to global properties [34].…”

Section: Introductionmentioning

confidence: 99%

Quantum information dynamics in a high-dimensional parity-time-symmetric system

et al. 2020

Self Cite

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Non-Hermitian systems with parity-time (PT) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second or higher order EPs have been proposed or realized. In contrast, quantum information studies of PT-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here by using a single-photon interferometry setup, we simulate quantum dynamics of a four-dimensional PT-symmetric system across a fourth-order exceptional point. By tracking the coherent, non-unitary evolution of the density matrix of the system in PT-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional PT-symmetric systems, and our results point towards the rich dynamics and critical properties.

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“…In order to achieve the maximal violation of CFFW inequality, we scan the whole permitted measurement strategies of Alice and Bob since the observables are unknown but keeping B 1 and B 2 mutually unbiased. In the experiment, we only need to add certain QWPs in the original measurement setup, namely, a combination of sandwich type QWP-HWP-QWP sequence [36][37][38], and a following PBS to realize the measurement operators. The coincidence counting of the APDs {D1, D3} represent the result a = b = 0, simultaneously.…”

Section: Experimental Demonstration and Resultsmentioning

confidence: 99%

Experimental Demonstration of Fine-Grained Steering Inequality of Two-Qubit Mixed States

Bian

Yin²

2021

Photonics

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Quantum steering, as a cornerstone of quantum information, is usually used to witness the quantum correlation of bipartite and multi-partite states. Here, we experimentally demonstrate the quantum steering inequality of two-qubit mixed states based on the fine-grained uncertainty relation. Our experimental results show that the steering inequality has potent sensitivity to Werner states and Bell diagonal states. The steering strategy exhibits a strong ability to identify that Werner states are steerable when the decoherence coefficient a>12. Compared to the steering inequality obtained by another stratagem, the steering witness criteria of mixed states based on the fine-grained uncertainty relation demonstrated in our experiment has better precision and accuracy. Moreover, the detection efficiency in our measurement setup is only required to be 50% to close the detection loophole, which means our approach needs less detector efficiency to certificate the steerability of mixed states.

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Conserved quantities in parity-time symmetric systems

Cited by 43 publications

References 37 publications

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Quantum information dynamics in a high-dimensional parity-time-symmetric system

Experimental Demonstration of Fine-Grained Steering Inequality of Two-Qubit Mixed States

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