Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics

Bagchi, B.; Barik, Suvendu

doi:10.1142/s021773232050090x

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…In addition, PT -symmetric system also shows practical vales in quantum sensors [22][23][24], which can use the sensitivity of PT -symmetric system near the exceptional points (EPs) to amplify small signals. In particular, it is worth noting that, with the increasing interest in PTsymmetric systems, some new phenomena have emerged [25,26], which are impressive because they seem to conflict with theory of conventional quantum mechanics or * gllong@mail.tsinghua.edu.cn theory of relativity, such as the instantaneous quantum brachistochrone problem [15,[27][28][29][30][31][32][33][34], the deterministical discrimination of nonorthogonal quantum states [35,36], and the violation of no-signaling principle [33,[37][38][39][40][41][42]. However, some anomalies actually come from not knowing how to simulate PT -symmetric system in conventional quantum system, for instance, if the discarded probabilities during the simulation of PT -symmetric system are considered, the no-signaling principle will still hold [43].…”

Section: Introductionmentioning

confidence: 99%

Dynamics simulation and numerical analysis of arbitrary time-dependent $\mathcal{PT}$-symmetric system based on density operators

Li¹,

Chen²,

Gao³

et al. 2022

Preprint

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PT -symmetric system has attracted extensive attention in recent years because of its unique properties and applications. How to simulate PT -symmetric system in traditional quantum mechanical system not only has basic theoretical significance, but also has practical application value. We proposal a dynamics simulation scheme of arbitrary time-dependent PT -symmetric system based on density operator. Based on that, we further study the influence of quantum noises on the simulation results with the technique of vectorization of density operator and matrixization of superoperators (VDMS), and we show the depolarizing (Dep) noise is the most fatal and should be avoided as much as possible. Meanwhile, we also give a numerical analysis of the above works. By theoretical analysis and numerical calculation, we find the problem of chronological product may have to be solved not only in numerical calculation, but also even in experiment, because the delated higher-dimensional Hamiltonian is usually time-dependent. And the solution of chronological product problem is actually one of the key factors to the accuracy of dynamics simulation of the time-dependent PT -symmetric system, and even the most key factor. We prove that the trusted duration of numerical calculation is actually bounded by the critical time Tc of convergence of Magnus series, while the implemented duration of experimental running is actually bounded by the critical time T l of legitimacy of dilation method.

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Section: Introductionmentioning

confidence: 99%

Dynamics simulation and numerical analysis of arbitrary time-dependent $\mathcal{PT}$-symmetric system based on density operators

Li¹,

Chen²,

Gao³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The interest for exploring the CHSH * game in non-Hermitian systems is that, in conventional quantum mechanics, Hermiticity is regarded as a fundamental assumption to guarantee some conventional quantum principles, such as entanglement monotonicity, [6,7] the no-signaling principle, [8,9] quantum speed limit, [10] and quantum indistinguishability between quantum states. [11] These principles obey Hermitian quantum mechanics unquestionably, but the violations of some principles were verified in non-Hermitian systems, particularly in 𝒫𝒯 -symmetric quantum systems, [8][9][10][12][13][14] which is proposed by Bender and colleagues in 1998. [15] Recently, 𝒫𝒯 symmetry has been constructed in quantum systems including single photons, [16] cold atoms, [17] and trapped ions, [18,19] etc.…”

mentioning

confidence: 99%

Non-Hermitian CHSH* Game with a Single Trapped-Ion Qubit

Song 宋,

Liu 刘,

Bian 边

et al. 2024

Chinese Phys. Lett.

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The Clauser-Horne-Shimony-Holt (CHSH) game provides a captivating illustration of the advantages of quantum strategies over classical ones. In a recent study, a variant of the CHSH game leveraging a single qubit system, referred to as the CHSH* game, has been identified. We demonstrate that this mapping relationship between these two games remains effective even for a non-unitary gate. In this context, we delve into the breach of Tsirelson’s bound in a nonHermitian system, predicting changes in the upper and lower bounds of the player’s winning probability when employing quantum strategies in a single dissipative qubit system. We experimentally explore the impact of the CHSH* game on the player's winning probability in a single trapped-ion dissipative system, demonstrating a violation of Tsirelson's bound under the influence of parity-time (PT) symmetry. These results contribute to a deeper understanding of the influence of non-Hermitian systems on quantum games and the behavior of quantum systems under PT symmetry, which is crucial for designing more robust and efficient quantum protocols.

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Efficient simulation of the dynamics of an n -dimensional PT -symmetric system with a local-operations-and-classical-communication protocol based on an embedding scheme

Zheng

Gao

et al. 2022

Phys. Rev. A

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Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics

Cited by 3 publications

References 29 publications

Dynamics simulation and numerical analysis of arbitrary time-dependent $\mathcal{PT}$-symmetric system based on density operators

Dynamics simulation and numerical analysis of arbitrary time-dependent $\mathcal{PT}$-symmetric system based on density operators

Non-Hermitian CHSH* Game with a Single Trapped-Ion Qubit

Efficient simulation of the dynamics of an n -dimensional PT -symmetric system with a local-operations-and-classical-communication protocol based on an embedding scheme

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