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Journal of Physics B Atomic Molecular and Optical Physics

Reversing the weak measurement on a qubit

M. Al-Amri, Marlan O. Scully, Muhammad Suhail Zubairy

Published Jul 29, 2011• 23 citations
Publisher

Abstract

We propose a protocol for the reversal of a weak measurement on a qubit and discuss a possible experimental scheme for the state protection in a cavity QED system. Unlike previous methods for the reversal of weak measurement, the proposed scheme does not require another weak measurement in the reversal process and therefore can be accomplished in a small time. The present scheme is based on repeated applications of Hadamard and CNOT gates.

DOI
10.1088/0953-4075/44/16/165509

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We propose a protocol for the reversal of a weak measurement on a qubit and discuss a possible experimental scheme for the state protection in a cavity QED system. Unlike previous methods for the reversal of weak measurement, the proposed scheme does not require another weak measurement in the reversal process and therefore can be accomplished in a small time. The present scheme is based on repeated applications of Hadamard and CNOT gates.
We present a proposal for reversing the weak (partial-collapse) quantum measurement on a cavity field with arbitrary maximum photon number. We start by putting forth a protocol to realize quantum phase gates between the cavity field and an ancilla qubit. Afterward, adopting these phase gates and some other quantum gates, we can determine the reversal of the cavity state just by observing the ancilla qubit. Compared to previous proposals, our proposal does not need any other weak measurement and can save reversal time, which is significantly important in quantum informatics and quantum computation.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Based on the quantum technique of the weak measurement and quantum measurement reversal (WMR), we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory, i.e., the amplitude damping channel, the phase damping channel, the bit flip channel, and the depolarizing channel. For a given initial state | ψ 〉 = a| 00 〉 + d| 11 〉, it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory, and the protection effect of WMR scheme is better when the coefficient a is small. For the other initial state | ϕ 〉 = b| 01 〉 + c| 10 〉, the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory. Moreover, the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective. For | ψ 〉 or | ϕ 〉, we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified. Another more important result is that the relationship between the concurrence, the memory parameter, the weak measurement strength, and quantum measurement reversal strength is found through calculation and discussion. It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.
Addressing various types of decoherence is of paramount importance for employing entanglement in quantum information processing and quantum computing. In this paper, we propose two schemes to manipulate entanglement of two qubits stored in a common environment by means of combined weak measurements and quantum measurement reversals. We derive the explicit conditions for the measurement strengths under which at any time and for any initial states the qubits' entanglement can be protected quite well with a reasonable finite success probability. Moreover, the two schemes enable us in principle to achieve the maximal entanglement or to restore the initial state (entanglement) of the qubits.