Sharing quantum indistinguishability with multiple parties

TL;DR

The paper develops and analyzes a sequential maximum-confidence measurement framework that lets multiple parties sequentially extract quantum indistinguishability from a single system. By combining maximum-confidence state discrimination with weak measurements, it shows how per-party confidence can be preserved under certain conditions (linearly independent POVMs) and how, for dependent ensembles, confidence gradually degrades while still enabling information sharing. The work provides explicit constructions for two mixed states and explores symmetric ensembles (geometrically uniform, lifted GU, and mirror-symmetric states) to illustrate geometry-preserving transformations and convergence behavior. It also formulates operational links to the max relative entropy and discusses potential applications in secure randomness generation and multi-party quantum information protocols. Overall, the results illuminate the limits and operational mechanisms of sequential information extraction in quantum systems and point to practical avenues for sequential resource sharing.

Abstract

Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme that enables multiple parties to share quantum uncertainty, in terms of the max relative entropy, generated by a single party. Our scheme is based upon maximum-confidence measurements and takes advantages of weak measurements to allow a number of parties to perform state discrimination on a single quantum system. We review known sequential state discrimination and show how our scheme would work through a number of examples where ensembles may or may not contain symmetries. Our results will have a role to play in understanding the ultimate limits of sequential information extraction and guide the development of quantum resource sharing in sequential settings.

Figures (7)

• Figure 1: The scenario of sequential maximum confidence measurements. One party prepares a state taken from the ensemble $\{q_x, \rho_x\}_{x=1}^N$. This system is then measured in turn by $R$ parties who each implements an MCM, updating the state to $\mathcal{E}^{(j)}(\rho_x)$ after each measurement, such that their confidence is $C_x^{(j)}$.
• Figure 2: Sequential maximum confidence measurements are applied to an ensemble of two mixed states. The effect is to increase the purity of the states while reducing the angle between them, see Eq. \ref{['eq:mixedsmcmkraus']}.
• Figure 3: Sequential MCM is implemented on an ensemble of symmetric states. After each measurement, the fixed angle between the states is preserved while the purity is decreased.
• Figure 4: Sequential MCM is implemented on an ensemble of geometrically uniform states. Party $j$ measures a confidence given by $2 P_+ / N$ (see Eq. \ref{['eq:symmjconf']}). The factor of proportionality $P_+$ is plotted for three different inconclusive rates: $\eta_0=0.9$ (green), $\eta_0=0.5$ (blue) and $\eta_0=0.1$ (red).
• Figure 5: Sequential maximum confidence measurements are applied to three lifted geometrically uniform states, as shown in Eq. \ref{['eq:liftgustates']}. The measurement causes the purity of each state to change while their angles with respect to the $Z$ axis is preserved.