Quantum Correlations in Mixed-State Metrology

TL;DR

This paper investigates how quantum correlations like entanglement and discord influence phase estimation efficiency in mixed states, demonstrating quantum strategies outperform classical ones even with high mixedness and non-entangled correlations.

Contribution

It introduces a comparative analysis of quantum and classical strategies for phase estimation considering mixedness, highlighting quantum advantage with non-entangled correlations.

Findings

Quantum strategies outperform classical ones with a square-root of N enhancement.

Quantum advantage persists even in highly mixed states without entanglement.

Nonclassical correlations, such as discord, contribute to improved metrological performance.

Abstract

We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated single-qubit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits) and time (number of gates) requirements, we introduce mixedness as a key constraint of the experiment. We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives square-root of N enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.