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arXiv:quant-ph/0701025 · Physical Review A

Probabilistic reversing operation with fidelity and purity gain for macroscopic quantum superposition

Hiroaki Terashima, Masahito Ueda

Published May 17, 2007• 5 citations
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Abstract

It is shown that a large class of weak disturbances on macroscopic quantum superpositions can be canceled by a probabilistic reversing operation on the system. We illustrate this for spin systems undergoing an Ising-type interaction with the environment and demonstrate that both the fidelity to the original state and the purity of the amended state can simultaneously be increased by the reversing operation. A possible experimental scheme to implement our scheme is discussed.

DOI
10.1103/physreva.75.052323

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It is shown that a large class of weak disturbances on macroscopic quantum superpositions can be canceled by a probabilistic reversing operation on the system. We illustrate this for spin systems undergoing an Ising-type interaction with the environment and demonstrate that both the fidelity to the original state and the purity of the amended state can simultaneously be increased by the reversing operation. A possible experimental scheme to implement our scheme is discussed.
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.
We propose a physically reversible quantum measurement of an arbitrary spin-sss system using a spin-jjj probe via an Ising interaction. In the case of a spin-1∕21∕21∕2 system (s=1∕2)(s=1∕2)(s=1∕2), we explicitly construct a reversing measurement and evaluate the degree of reversibility in terms of fidelity. The recovery of the measured state is pronounced when the probe has a high spin (j>1∕2)(j>1∕2)(j>1∕2), because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin-1∕21∕21∕2 system can serve as an experimentally feasible approximate reversing measurement for a high-spin system (s>1∕2)(s>1∕2)(s>1∕2). If the interaction is sufficiently weak, the reversing measurement can recover a cat state almost deterministically in spite of there being a large fidelity change.
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 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.
Entanglement of a system changes due to interactions with the environment. A typical type of interaction is amplitude damping. If we add a detector to monitor the environment and only select the no-damping outcome, this amplitude damping is modified into a weak measurement. Here we show that the entanglement change of a two-qubit state due to amplitude damping or weak measurement can be probabilistically reversed. For the amplitude-damping case, the entanglement partially recovers under most conditions. For the weak-measurement case, the recovery of the initial entangled state is exact. The reversal procedure involves another weak measurement, preceded and followed by bit flips applied to both qubits. We propose a linear optics scheme for the experimental demonstration of these procedures.