Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States

TL;DR

This paper explores the fundamental limits of local strategies in discriminating entangled quantum states, revealing a trade-off between information gain and disturbance, and proposes an adaptive, non-destructive discrimination method that outperforms traditional approaches.

Contribution

It introduces a new trade-off relation for local state discrimination of entangled states and proposes an adaptive, non-destructive strategy leveraging stabilizer formalism.

Findings

Local strategies are limited by a trade-off between information gain and disturbance.

Pre-shared entanglement can circumvent the trade-off.

The proposed strategy reduces entanglement cost compared to teleportation-based methods.

Abstract

We establish an information gain-disturbance trade-off relation in local state discrimination. Our result demonstrates a fundamental limitation of local strategy to discriminate entangled quantum states without disturbance, which becomes more difficult as the entanglement of the states to be discriminated increases. For a set of maximally entangled states, the capability of local strategy is tightly suppressed, as random guessing without measurements saturates the bound provided by the trade-off relation. We also show that the trade-off can be circumvented when local operations are aided by pre-shared entanglement. To simultaneously achieve correct guessing of state and non-disturbance, an entirely different strategy from conventional state discrimination should be adopted to lower the cost of pre-shared entanglement. We explicitly propose an adaptive and non-destructive strategy based on the stabilizer formalism, which shows a strict advantage over conventional teleportation-based approaches in pre-shared entanglement cost for discriminating a set of maximally entangled states. As an application of the trade-off relation, we propose an entanglement certification protocol that is robust against depolarizing noise and generalize it to multipartite scenarios in a quantum network.