Improving the Robustness of Entangled States by Basis Transformation.

Xin-Wen Wang,Shi-Qing Tang,Yan Liu,Ji-Bing Yuan

doi:10.3390/e21010059

Xin-Wen Wang, Shi-Qing Tang + Show 2 more

Open Access

https://doi.org/10.3390/e21010059

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Abstract

In the practical application of quantum entanglement, entangled particles usually need to be distributed to many distant parties or stored in different quantum memories. In these processes, entangled particles unavoidably interact with their surrounding environments, respectively. We here systematically investigate the entanglement-decay laws of cat-like states under independent Pauli noises with unbalanced probability distribution of three kinds of errors. We show that the robustness of cat-like entangled states is not only related to the overall noise strength and error distribution parameters, but also to the basis of qubits. Moreover, we find that whether a multi-qubit state is more robust in the computational basis or transversal basis depends on the initial entanglement and number of qubits of the state as well as the overall noise strength and error distribution parameters of the environment. However, which qubit basis is conductive to enhancing the robustness of two-qubit states is only dependent on the error distribution parameters. These results imply that one could improve the intrinsic robustness of entangled states by simply transforming the qubit basis at the right moment. This robustness-improving method does not introduce extra particles and works in a deterministic manner.

Highlights

Quantum entanglement, a typical non-classical correlation between quantum systems, is at the center of quantum information science [1,2,3,4]
The problem on how to harness entanglement of quantum systems against the detrimental effects of the environment is of utmost importance within the vast domain of studies of quantum entanglement, since it is directly connected to the applications of quantum entanglement [13,14]
It was shown that the decay law of a cat-like state is related to the overall noise strength (p), and to the error distribution parameters, and that the robustness of both two-qubit and multi-qubit states in a given noisy environment is dependent on the basis of qubits

Summary

Introduction

A typical non-classical correlation between quantum systems, is at the center of quantum information science [1,2,3,4]. Depolarizing noise acting on physical qubits encoding a logical qubit could be modeled as effective Pauli noise, with unbalanced probability distribution for the three errors, acting on the logical qubit [53]. Another example is provided by thermal baths with infinite temperature, where the decoherence of a qubit can be described by a Pauli map with a x = ay 6= az [12,44]. Cat-like entangled states under the local (independent) Pauli channels where the probabilities of three kinds of errors occurring are not the same. Two-qubit entangled states may exhibit the opposite phenomenon to multi-qubit entangled states

Robustness of Cat-Like States and Its Enhancement Method

Robustness of Cat-Like States in the Computational Basis

Robustness of Cat-Like States in the Transversal Basis

Enhancing the Robustness of Cat-Like States by Basis Transformation

Conclusions