Information, fidelity, and reversibility in photodetection processes

Abstract

Four types of photon counters are discussed in terms of information, fidelity, and physical reversibility: conventional photon counter, quantum counter, and their quantum nondemolition (QND) versions. It is shown that when a photon field to be measured is in an arbitrary superposition of vacuum and one-photon states, the quantum counter is the most reversible, the QND version of conventional photon counter provides the most information, and the QND version of quantum counter causes the smallest state change. Our results suggest that the physical reversibility of a counter tends to decrease the amount of information obtained by the counter.Comment: 34 pages, 8 figure

Information, fidelity, and reversibility in general quantum measurements

“…Such tradeoffs have been studied in photodetection processes [34] and in single-qubit measurements [35]. These tradeoffs are at the level of a single outcome, in contrast to conventional ones [6,7,9,10,14,16]; that is to say that the quantities affected are those pertaining to each single outcome, rather than those averaged over all possible outcomes.…”

Balance Between Information Gain and Reversibility in Weak Measurement

“…In this sense, the extracted information should be more tightly related to the possibility of undoing the measurement [4] rather than the closeness between input and post-measurement states as used in previous works [2]. Recently, an entropic tradeoff relation was derived based on the concept of information conservation in measurement process [18], and a degree of information gain was investigated by changing the reversibility in a single measurement outcome level [19]. However, a clear and direct quantitative relation between information gain and reversibility in quantum measurement has so far been missing.…”

“…From Eq. (19), the erasing operator for 2 (whereD −1 = |0 0| + (1/ √ 1 − η) |1 1| and λ 2 1 = √ 1 − η) is given aŝ…”

Information and fidelity in projective measurements

“…This feature originates from the fact that the physical reversibility of measurements suggests quantifying the information gain and the state change for each single outcome, because in physically reversible measurements, a state recovery with information erasure (see the Erratum of [22]) occurs because of the post-selection of outcomes. However, the explicit calculations in the previous studies [16,17] were only performed with two-level systems or qubits.…”