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arXiv:quant-ph/0507020 · Physical Review A

Reversible quantum measurement with arbitrary spins

Hiroaki Terashima, Masahito Ueda

Published Jul 17, 2006• 11 citations

Abstract

We propose a physically reversible quantum measurement of an arbitrary spin-$s$ system using a spin-$j$ probe via an Ising interaction. In the case of a spin-$1∕2$ system $(s=1∕2)$, 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 $(j>1∕2)$, because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin-$1∕2$ system can serve as an experimentally feasible approximate reversing measurement for a high-spin system $(s>1∕2)$. 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.

DOI: 10.1103/physreva.74.012102

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We propose a physically reversible quantum measurement of an arbitrary spin-

s

system using a spin-

j

probe via an Ising interaction. In the case of a spin-

1∕2

system

(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)

, 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∕2

system can serve as an experimentally feasible approximate reversing measurement for a high-spin system

(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 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 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.

A measurement procedure on a spin 1/2 system is described, whose effect on the (possibly unknown) state of the system can be reversed, by means of other similar measurements, with a sizable probability of success

{P}^{\mathrm{rev}}

(e.g.,

\frac{1}{2}<{P}^{\mathrm{rev}}<1

, depending on the state). Repeated such measurements followed by reversal, on a single system, allow us to determine its (a priori unknown) state operator with a probability of success which is nonzero, though extremely small (because

{P}^{\mathrm{rev}}<1

).

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.