Chaos-Mediated Quantum State Discrimination Near Unit Fidelity

TL;DR

This paper proposes a quantum microscope leveraging chaotic dynamics and Bell correlations to exponentially amplify small state differences, enhancing quantum state discrimination near perfect fidelity.

Contribution

It introduces a novel method combining chaos and Bell correlations to improve quantum state discrimination beyond traditional limits.

Findings

Exponential amplification of fidelity differences using chaos.

Bell-type correlations detect minute initial state differences.

Discrimination efficiency depends on the waiting time for divergence.

Abstract

We investigate a ''quantum microscope'' for qubits based on nonlinear discrete-time chaotic dynamics, which exponentially amplifies the initially small fidelity of a pair of states to a large saturation value ( $\sim$ 1/2), thereby pushing the Helstrom bound to more accessible values. We show that Bell-type temporal correlations can capture even the minutest differences between two initial states, thus enabling their distinguishability. The cost of distinguishability is quantified in terms of the characteristic waiting time of the evolution, defined as the time after which the temporal correlation of a given initial state begins to diverge exponentially from that of a nearby state. The closer the two states are, the longer this waiting time becomes. By combining chaos with Bell-type temporal correlations, this approach opens unexplored avenues for pushing the limits of precision in quantum metrology.