Quantum change point and entanglement distillation

TL;DR

This paper investigates quantum change point detection in entangled sources using LOCC, demonstrating protocols for identifying change points and distilling entanglement, with success depending on the orthogonality and distinguishability of states.

Contribution

It introduces LOCC-based protocols for quantum change point detection in entangled sources, analyzing success probabilities and entanglement distillation under various state orthogonality conditions.

Findings

Efficient LOCC protocol for orthogonal states with guaranteed change point identification.

Probability of failure when states are nonorthogonal, with average entangled pairs quantified.

Local distinguishability determines whether the problem reduces to a simpler two-state scenario.

Abstract

In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles emitted from such a source. Motivated by entanglement-sharing protocols in quantum information, we study this problem within the paradigm of local operations and classical communication (LOCC). Here, we consider a source that emits entangled pairs in a default state, but starts producing another entangled state (mutation) at a later stage. Then, a sequence of entangled pairs prepared from such a source and shared between distant observers cannot be used for quantum information processing tasks as the identity of each entangled pair remains unknown. We show that identifying the change point using LOCC leads to the distillation of free entangled pairs. In particular, if the default and the mutation are mutually orthogonal, there exists an efficient LOCC protocol that identifies the change point without fail and distills a sufficiently large number of pairs. However, if they are nonorthogonal, there is a probability of failure. In this case, we compute the number of entangled pairs that may be obtained on average. We also consider a relaxation of the two-state problem where the mutation is not known a priori, but instead belongs to a known set. Here we show that local distinguishability plays a crucial role: if the default and the possible mutations are locally distinguishable, the problem reduces to the two-state problem with orthogonal states, but if not, one may still identify the mutation, the change point, and distill entanglement, as we illustrate with a concrete example.