Recycling of quantum information: Multiple observations of quantum systems

TL;DR

This paper demonstrates that even after optimal measurements, some information about an unknown quantum state can still be extracted by subsequent observers, challenging the notion that measurements completely erase prior information.

Contribution

It provides a quantitative analysis of information retrieval from quantum states after measurement, including multiple observers and extensions to various states.

Findings

Information can be partially recovered after measurement.

Optimal protocols for extracting residual information are identified.

Multiple observers can sequentially obtain meaningful information.

Abstract

Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information.