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Chinese Physics B

Reversion of weak-measured quantum entanglement state*

Shao-Jiang Du, Yonggang Peng, Hairan Feng, Feng Han, Lian-Wu Yang, Yujun Zheng

Published Apr 23, 2020• 7 citations
Publisher

Abstract

We theoretically study the reversible process of quantum entanglement state by means of weak measurement and corresponding reversible operation. We present a protocol of the reversion operation in two bodies based on the theory of reversion of single photon and then expend it in quantum communication channels. The theoretical results demonstrate that the protocol does not break the information transmission after a weak measurement and a reversible measurement with the subsequent process in the transmission path. It can reverse the perturbed entanglement intensity evolution to its original state. Under the condition of different weak measurement intensity the protocol can reverse the perturbed quantum entanglement system perfectly. In the process we can get the classical information described by information gain from the quantum system through weak measurement operation. On the other hand, in order to realize complete reversibility, the classical information of the quantum entanglement system must obey a limited range we present in this paper in the reverse process.

DOI
10.1088/1674-1056/ab8c3e

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We theoretically study the reversible process of quantum entanglement state by means of weak measurement and corresponding reversible operation. We present a protocol of the reversion operation in two bodies based on the theory of reversion of single photon and then expend it in quantum communication channels. The theoretical results demonstrate that the protocol does not break the information transmission after a weak measurement and a reversible measurement with the subsequent process in the transmission path. It can reverse the perturbed entanglement intensity evolution to its original state. Under the condition of different weak measurement intensity the protocol can reverse the perturbed quantum entanglement system perfectly. In the process we can get the classical information described by information gain from the quantum system through weak measurement operation. On the other hand, in order to realize complete reversibility, the classical information of the quantum entanglement system must obey a limited range we present in this paper in the reverse process.
We demonstrate the conditional reversal of a weak (partial-collapse) quantum measurement on a photonic qubit. The weak quantum measurement causes a nonunitary transformation of a qubit which is subsequently reversed to the original state after a successful reversing operation. Both the weak measurement and the reversal operation are implemented linear optically. The state recovery fidelity, determined by quantum process tomography, is shown to be over 94% for partial-collapse strength up to 0.9. We also experimentally study information gain due to the weak measurement and discuss the role of the reversing operation as an information erasure.
We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the information gain and reversibility. In this formulation, it is clearly shown that the information extracted from a weak measurement is erased through the reversing process. Our result broadens the information-theoretic perspective on quantum measurement as well as provides a standard tool to characterize weak measurements and reversals.
The entanglement properties of the quantum channel in quantum communication did not play well, in order to realize quantum communication at superluminal speed with the help of this entanglement property, a kind of quantum communication mode which can measure the change of quantum information is proposed in this article. This method can bypass the classical channel part in the quantum communication. In the concrete realization process, by combining the quantum weak measurement method, information transmission can be carried out without destroying entangled states, so as to achieve superluminal communication.
Liao Xiang-Ping et al.(Chin. Phys. B 23 020304, 2014) pointed out that the method of weak measurement and quantum weak measurement reversal can protect entanglement and improve the fidelity of three-qubit quantum state. We generalize the method of weak measurement to the case of qudit state in this paper. By using the operation of weak measurement and quantum weak measurement reversal, we investigate the evolution dynamics of fidelity and fidelity improvement for qudit state under amplitude damping decoherence. We compare two kinds of operations: one is to let the input qudit state cross the amplitude damping decoherence directly, and the other one is that we first make a weak measurement operation on the input qudit state, then through the amplitude damping decoherence, finally an operation of quantum weak measurement reversal is done with the output qudit state. We discuss the GHZ state, W state, CL state and some special separable states exactly and obtain the analytic expressions of fidelity and fidelity improvement for qudit state before and after the weak measurement and quantum weak measurement reversal operation. According to the analytic expressions we plot the evolution curves against its corresponding parameters. The effects of corresponding parameters are discussed and a susceptible protection region of the qudit state is also given in the context. The results show that the structure of qudit state is the determined factor to the effect of weak measurement and quantum weak measurement reversal. There are some different effects on the different structured qudit states. For entangled state, the fidelity of qudit GHZ state can be protected in a relatively big evolution region, most part of the fidelity improvement is in the upper part of the zero reference plane. While the fidelity of qudit W state can be improved effectively in the whole evolution region, which is a perfect protection. The evolution regulations of qudit CL state and Dick state are between evolution regulations of the GHZ state and W state. When we input some special separable qudit states which have similar structures to W state, their fidelity and fidelity improvement are almost the same as W state’s. It is demonstrated that the structure of qudit state is important for the weak measurement in a step. This work is meaningful for the quantum information process.
An upper bound between the information gain and state reversibility of weak measurement was first developed by Y. K. Cheong and S. W. Lee [Phys. Rev. Lett. 109, 150402 (2012)]. Their results are valid for arbitrary d-level quantum systems. In light of the commonly used qubit system in quantum information, a sharp tradeoff relation can be obtained. In this letter, this tradeoff relation is experimentally verified with polarization encoded single photons from a quantum dot. Furthermore, a complete traversal of weak measurement operators is realized, and the mapping to the least upper bound of this tradeoff relation is obtained. Our results complement the theoretical work and provide a universal ruler for the characterization of weak measurements.