Reversible quantum measurement with arbitrary spins

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.

Information, fidelity, and reversibility in photodetection processes

“…A quantum measurement is said to be physically reversible [7,9] if the premeasurement state can be recovered from the postmeasurement state with a nonzero probability of success by means of a second measurement, referred to as reversing measurement. Recently, physically reversible measurements have been proposed with various systems [10][11][12][13][14][15][16] and discussed in the context of quantum computation [17,18], and have been experimentally demonstrated using a superconducting phase qubit [19] and a photonic qubit [20]. Therefore, it would be worth discussing the state change by a measurement together with its physical reversibility.…”

Hermitian conjugate measurement

“…Note that this measurement {Ĉ (m) µ } can also be regarded as a reversing measurement with the preferred outcome ν 0 = −m if s = 1/2 [12], becausê…”

“…In fact, an approximate recovery with additional information gain was first reported [12] regarding the reversing measurement without identifying the origin of the information gain. The origin is now clarified in terms of the Hermitian conjugate measurement.…”

“…Although such a change in state was widely believed to be intrinsically irreversible [1], it has been shown that quantum measurement is not necessarily irreversible [2], because a certain class of measurements preserves all the information about the system during the measurement process. In recent work [2][3][4][5][6][7][8][9][10][11][12][13][14] on reversibility in quantum measurements, probabilistic reversing operations based on the inverse operator ofM [4,5,[8][9][10][11][12][13] have been discussed, whereM is an operator describing the state change due to the measurement. That is, a second measurement is performed on the system so that it appliesM −1 to the system state to cancel the effect ofM, when a preferred outcome is obtained.…”

“…[12]. However, the article did not identify the reason for the information gain because it focused on a reversing operation byM −1 .…”