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Chinese Physics B

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

Shi-Yang Zhang, Mao-Fa Fang, Yanliang Zhang, You-neng Guo, Yan-Jun Zhao, Wu-Wei Tang

Published Sep 1, 2015• 17 citations
Publisher

Abstract

We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with -symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local -symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian -symmetric operation.

DOI
10.1088/1674-1056/24/9/090304

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We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with -symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local -symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian -symmetric operation.
We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with PT-symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local PT-symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian PT-symmetric operation.
Abstract Considering one of the particles as a quantum memory in a bipartite system can remarkably improve the measurement accuracy for two incompatible observables. Herein, we study quantum-memory-assisted entropic uncertainty bound for an arbitrary two-qubit X-state, and then we get a clear formula as the entropic uncertainty bound. In the following, we examine analytically and numerically the dynamics of entropic uncertainty bound in a symmetric multi-qubit system under four types of noisy channels, i.e. phase-flip, amplitude damping, phase-damping, and depolarizing channels. Our results show that the entropic uncertainty bound dynamics is related to the number of particles and especially the noise channel used. Noteworthy, our remarks reveal that under the amplitude damping channel, the entropic uncertainty bound can be suppressed during the time. It turns out that under an amplitude damping channel, these results can be important in practical goals where the minimum uncertainty is required such as quantum computation.
Abstract Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.
We have investigated the dynamic features of the quantum-memory-assisted entropic uncertainty relation (QMA EUR) in the amplitude damping (AD) channel. The initial state of qubit system and quantum memory system shared between Alice and Bob is assumed as extended by Werner-like (EWL) state. To reduce the amount of entropic uncertainty of Pauli observables in this noisy channel, we presented a reduction scheme by means of weak measurements (WMs) and weak measurement reversals (WMRs) before and after the entangled system subjecting to the noisy channel. It is shown that the prior WM and poster WMR can effectively reduce quantity of entropic uncertainty, but the poster WM operation cannot played a positive role on reduction of quantity of entropic uncertainty. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory. In this work, we explore the behavior of the quantum-memory-assisted entropic uncertainty relation under the influence of local unital and nonunital noisy channels. For a class of Bell-diagonal states, we demonstrate that while the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may reduce the amount of uncertainty in the long-time limit. The mechanism behind this phenomenon is also explored by using two dissimilar methods.
Abstract The uncertainty principle is viewed as one of the appealing properties in the context of quantum mechanics, which intrinsically offers a lower bound with regard to the measurement outcomes of a pair of incompatible observables within a given system. In this letter, we attempt to observe entropic uncertainty in the presence of quantum memory under different local noisy channels. To be specific, we develop the dynamics of the measured uncertainty under local bit-phase-flipping (unital) and depolarization (nonunital) noise, respectively, and attractively put forward an effective strategy to manipulate its magnitude of the uncertainty of interest by means of parity-time symmetric ( -symmetric) operations on the subsystem to be measured. It is interesting to find that there exist different evolution characteristics of the uncertainty in the channels considered here, i.e. the monotonic behavior in the nonunital channels, and the non-monotonic behavior in the unital channels. Moreover, the amount of the measured uncertainty can be reduced to some degree by properly modulating the -symmetric operations.