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Physical Review A

Efficacy of measurement reversal for stochastic disturbances

David J. Starling, Nathan S. Williams

Published Aug 30, 2013• 5 citations
Publisher

Abstract

We analyze the statistical properties of entanglement for pairs and triples of entangled qubits subject to a random disturbance followed by restoration. After the random disturbance, which is modeled as a null-result weak measurement, the state is restored by applying a static measurement reversal. We then show that the fidelity of the resulting state, and therefore its entanglement, can be restored with a high success, despite the statistical fluctuations of the disturbance. In particular, we show that the variance of the entanglement of an ensemble of restored states is substantially reduced, despite large disturbances. We conclude with a proposed experimental implementation.

DOI
10.1103/physreva.88.024304

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We analyze the statistical properties of entanglement for pairs and triples of entangled qubits subject to a random disturbance followed by restoration. After the random disturbance, which is modeled as a null-result weak measurement, the state is restored by applying a static measurement reversal. We then show that the fidelity of the resulting state, and therefore its entanglement, can be restored with a high success, despite the statistical fluctuations of the disturbance. In particular, we show that the variance of the entanglement of an ensemble of restored states is substantially reduced, despite large disturbances. We conclude with a proposed experimental implementation.
We propose a class of probabilistic reversing operations on the state of a system that was disturbed by a weak measurement. It can approximately recover the original state from the disturbed state especially with an additional information gain using the Hermitian conjugate of the measurement operator. We illustrate the general scheme by considering a quantum measurement consisting of spin systems with an experimentally feasible interaction and show that the reversing operation simultaneously increases both the fidelity to the original state and the information gain with such a high probability of success that their average values increase simultaneously.
Abstract The effect of environment-assisted measurement and quantum measurement reversal on the entanglement transfer in two parallel Heisenberg spin chains is investigated. We derive the exact analytical expression of the optimal final restoration, show that the distribution entanglement could be restored to the initial value, which is independent of the size of the spin chain. Comparing with the results obtained by the method of weak measurement, our results show notable superiorities on restoration scope and success probability.
Abstract Based on the quantum technique of environment-assisted measurement and reversal (EMR), we propose a scheme to restore the entanglement from amplitude damping decoherence. In particular, we examine two typical families of initially entangled qubit–qutrit states and derive the exact analytical expressions of the optimal final restoration, showing explicitly that the EMR does indeed can recovery qubit–qutrit entanglement. This sheds new light on the protection of high-dimensional quantum entanglement in complex quantum environment.
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.
Abstract We examine the validity of the environment-assisted measurement (EAM) and quantum measurement reversal (QMR) operations in the restoration of distributed entanglement for two-qubit transmission under three typical kinds of noisy quantum channels, i.e. an amplitude damping channel, a phase damping channel and a depolarizing quantum channel. Given the parameters of the Bell-like initial qubits’ state and , we derive exact expressions for the optimal final quantum entanglement, showing explicitly that combining the EAM and QMR operations does indeed help in recovering the distributed entanglement from the various decoherence sources. Comparing with the results obtained using the weak measurement and QMR method, our results show notable superiorities in adaptation scope and success probability.
Abstract Maximal quantum entanglement provided by N00N states is a unique resource in the quest for the ultimate precision in physical measurements. Such states, however, are fragile and prone to decoherence. Even in weak-measurement schemes, as we demonstrate in this work, the phase super-resolution provided by N00N states is achieved at a cost of an N -fold enhancement of amplitude damping. Still, as the analysis presented here shows, a partial collapse of N00N states induced by weak measurements can be reversed, despite the dramatic, N -fold enhancement of amplitude damping, through appropriate reversal operations on the post-measurement state, enabling a full restoration of the Heisenberg-limit phase super-resolution of N00N states.