Quantum Correlations in Mixed-State Metrology

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 ffiffiffiffi N p 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.

Measures and applications of quantum correlations

“…The authors of [266] investigated unitary phase estimation using N-qubit probe states (with phase transformation applied to each qubit) initialised in mixed states with a) no correlations; b) only classical correlations; or c) non-classical correlations (QCs or entanglement); all classes of probe states having the same (tunable) degree of purity for fairness of comparison. They found that uncorrelated and classically correlated probes resulted in a quantum Fisher information scaling linearly with N, while quantum strategies allowed for a quadratic scaling N 2 , as expected in quantum metrology [263].…”

Supraclassical measurement using single-atom control of an atomic ensemble

“…The scheme is related to those in Refs. [8,9], and the specific implementation we consider is based on quantum correlations between a single "clean" (nearly pure) control qubit and a register of partially mixed register qubits, using a platform similar to the one described in Ref. [12].…”

“…A new perspective on the resources required to achieve a quantum advantage for measurement precision is provided by two theoretical works which investigate mixed-state models of quantum metrology [8,9]. Reference [8] compares quantum probes, which can be prepared using unitary circuits, from initial qubits, which are mixed, uncorrelated, and identical.…”

“…Reference [8] compares quantum probes, which can be prepared using unitary circuits, from initial qubits, which are mixed, uncorrelated, and identical. For a given number of qubits and fixed purity, it was found that circuits generating quantum correlations can achieve a quadratic enhancement in the measurement precision (compared to the use of the initial qubits as separate probes).…”

Quantum Sensing of Noisy and Complex Systems under Dynamical Control

“…Such probes are amenable to quantum-mechanical description even though their quantumness, i.e., quantum coherence or entanglement, may or may not play a role in the sensing process. If the goal is to acquire quantum information (QI), i.e., read out the state of the probed system, then measurements of quantum correlations within or among probes become indispensable [1]. We, however, focus here on the much more robust and readily obtainable classical information on the system by simple quantum probes: either single or correlated qubits that are engineered to possess advantageous properties for the sensing process in question: Thus, superconducting qubits are excellent detectors of microwave or far-infrared photons [2]; Rydberg-atom qubits are highly sensitive probes of dipolar forces; and nitrogen-vacancy centers (NVC) in diamond are the most sensitive magnetometers or electrometers to date [3][4][5][6][7].…”