Reduction of entropic uncertainty in entangled qubits system by local 𝒫𝒯-symmetric operation

Zhang, Shiyang; Mao-Fa, Fang; Zhang, Yanliang; Guo, You-neng; Zhao, Yixin; Tang, Wu-Wei

doi:10.1088/1674-1056/24/9/090304

“…In recent years, parity-time (𝒫𝒯 ) symmetry has attracted increasing attention in non-Hermitian quantum mechanics. [1][2][3][4][5][6][7][8][9][10][11] 𝒫𝒯 -symmetric non-Hermitian systems, which may possess entirely real spectra, [12] have been widely explored in the optical waveguides, resonators, and cold atoms in optical lattices. The exceptional point (EP), known as the 𝒫𝒯 -symmetric phase transition point, indicates the transition between the exact 𝒫𝒯 -symmetric phase and the broken 𝒫𝒯symmetric phase.…”

Section: Introductionmentioning

confidence: 99%

Topology of a parity–time symmetric non-Hermitian rhombic lattice

Zhang¹,

Jin²,

Song³

2022

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We investigate the topological properties of a trimerized parity–time ( P T ) symmetric non-Hermitian rhombic lattice. Although the system is P T -symmetric, the topology is not inherited from the Hermitian lattice; in contrast, the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices. The bulk–boundary correspondence is valid and the Bloch bulk captures the band topology. Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach. In addition, the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice. Our findings reveal the topological properties of the P T -symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.

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“…[13] the authors found that the nosignalling principle can be violated when applying the local PT -symmetric operation on one of the entangled particles. More recently, it has also been shown that PT -symmetric operation can be used to suppress the decoherence of amplitude damping model, [14][15][16][17][18][19][20] and slow down the decoherence of pure phase damping model. [21] On the other hand, the entanglement of assistance (EOA) [22,23] as a special case of the localizable entanglement [24] has recently attracted intense attention, [25][26][27][28][29][30][31] which quantifies the entanglement that can be generated between two parties, Alice and Bob, given assistance from a third party, Charlie, when three of them share a tripartite state and where the assistance consists of Charlie initially performing a measurement on his share and communicating the result to Alice and Bob through a one-way classical channel.…”

Section: Introductionmentioning

confidence: 99%

Improving entanglement of assistance by local parity–time symmetric operation*

He

¹

,

Nie

²

,

Wang

³

2019

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We investigate entanglement of assistance without and with decoherence using a local non-Hermitian operation, i.e., parity–time ( P T ) symmetric operation. First we give the explicit expressions of entanglement of assistance for a general W-like state of a three-qubit system under a local parity–time symmetric operation. Then for a famous W state without decoherence, we find that entanglement of assistance shared by two parties can be obviously enhanced with the assistance of the third party by a local parity–time symmetric operation. For the decoherence case, we provide two schemes to show the effects of local parity–time symmetric operation on improvement of entanglement of assistance against amplitude damping noise. We find that for the larger amplitude damping case the scheme of P T symmetric operation performed on one of two parties with the influence of noise is superior to that of P T symmetric operation performed on the third party without the influence of noise in suppressing amplitude damping noise. However, for the smaller amplitude damping case the opposite result is given. The obtained results imply that the local P T symmetric operation method may have potential applications in quantum decoherence control.

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“…[11,12] Owing to its appealing perfor-mance, the entropic uncertainty relation has attracted much attention. Some quantum operations of quantum states are proposed for stable systems, quantum correlation protection and the reduction of entropic uncertainty, [13][14][15][16][17][18][19] for example, the behavior of QMA-EUR under different noise, the relations between the QMA-EUR and teleportation and entanglement evidence, [20] and the influence of quantum discord and classical correlation on entropic uncertainty in the presence of quantum memory. [21,22] In addition, QMA-EUR has many potential applications in the field of quantum information science, including quantum metrology, [23] quantum transition, [24,25] quantum key distribution, [26] cryptography, and quantum randomness.…”

Section: Introductionmentioning

confidence: 99%

Influence of homodyne-based feedback control on the entropic uncertainty in open quantum system*

Hu

¹

,

Xue

²

2019

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For an open quantum system containing two qubits under homodyne-based feedback control, we investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty. Moreover, we analyze the influence of feedback modes and coefficients on the entropic uncertainty. Numerical investigations show that the memory qubit should be placed in a non-dissipative channel if the single dissipative channel condition can be chosen, which helps reduce the entropic uncertainty of the system. For the homodyne feedback control F = λ σ x (or F = λ σ y ) , due to different roles of the entangled qubits A and B, when they are subject to feedback control with different feedback coefficients λ, the exchange of feedback coefficients will cause variations of the entropic uncertainty. When the feedback coefficient corresponding to the memory qubit B is larger ( λ B > λ A ) , the steady value of the entropic uncertainty will be small, which is conducive to enhancing the robustness of the system. However, for the feedback control F = λ σ z , the difference between the feedback coefficients has no effect on the steady values of the entropic uncertainty.

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Reduction of entropic uncertainty in entangled qubits system by local 𝒫𝒯-symmetric operation

Cited by 12 publications

References 37 publications

Topology of a parity–time symmetric non-Hermitian rhombic lattice

Topology of a parity–time symmetric non-Hermitian rhombic lattice

Improving entanglement of assistance by local parity–time symmetric operation*

Influence of homodyne-based feedback control on the entropic uncertainty in open quantum system*

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