Hermitian conjugate measurement

Abstract

We propose a new 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.Comment: 26 pages, 4 figures; a paragraph is added in the introductio

Information, fidelity, and reversibility in photodetection processes

“…[11]), although a physically reversible measurement actually provides some information about the measured system, in contrast to the unitarily reversible measurements [21,22]. Therefore, a reversing operation based onM † , instead ofM −1 , has been proposed [23] which can approximately recover the premeasurement state, especially with increasing, rather than decreasing, information gain for a weak measurement. Further discussions of information gain by a physically reversible measurement can be seen in other studies [24,25].…”

“…Among the four counters, the quantum counter and its QND version are physically reversible. For each counter we evaluate the amount of information gain using a decrease in Shannon entropy [23,25], the degree of state change using fidelity [29], and the degree of physical reversibility using the maximal successful probability of reversing measurement [17], assuming that a photon field to be measured is in an arbitrary superposition of vacuum and one-photon states.…”

Allowed region and optimal measurement for information versus disturbance in quantum measurements

“…Therefore, I(m), which we define as the information gain, quantifies the amount of information provided by the outcome m of the measurement {M m } [11,37] and is explicitly written in terms of the singular values of M m as [26]…”

Information and fidelity in projective measurements

“…. , N, with equal probability p(a) = 1/N [16,17,33], although the index a of the pre-measurement state is unknown to us. Thus, the lack of information about the state of the system can be evaluated by Shannon entropy as…”

“…. , θ 2d−2 , φ) as [33] α 1 (a) = sin θ 2d−2 sin θ 2d−3 · · · sin θ 3 sin θ 2 sin θ 1 cos φ, where 0 ≤ φ < 2π and 0 ≤ θ p ≤ π with p = 1, 2, . .…”