Scavenging quantum information: Multiple observations of quantum systems

TL;DR

This paper investigates how multiple independent observers can sequentially extract information from a quantum system, revealing the limits and strategies for information scavenging in quantum measurements.

Contribution

It provides closed-form formulas for estimation fidelity in sequential measurements and explores optimal measurement strategies for multiple observers.

Findings

Sequential measurements allow information scavenging with diminishing fidelity.

Closed-form expressions for estimation fidelity in various measurement scenarios.

Optimal strategies enable nearly complete information extraction with multiple observers.

Abstract

Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system `collapses' into a post-measurement state from which the {\em{same}} observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity, when one or several qudits are available to carry information about the single-qudit state, and study the `classical' limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements we study the scenario where a finite number of observers estimate the state with equal fidelity,regardless of their position in the measurement sequence; and the scenario where all observers use identical measurement apparata (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.