On the Optimal Choice of Spin-Squeezed States for Detecting and Characterizing a Quantum Process

TL;DR

This paper investigates the optimal quantum states, especially group-covariant 2-designs, for detecting and characterizing unknown quantum processes using biphoton states, balancing sensitivity and informational completeness.

Contribution

It identifies and experimentally confirms the best group-covariant probe states for quantum process tomography, which are less entangled than N00N states but more effective for characterization.

Findings

Maximally entangled N00N states are highly sensitive to SU(2) rotations.

Group-covariant 2-design states optimize process characterization.

Experimentally validated the effectiveness of these states for quantum process tomography.

Abstract

Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything. This requires quantum process tomography, which demands an informationally-complete set of probe states. It is very convenient if this set is group-covariant -- i.e., each element is generated by applying an element of the quantum system's natural symmetry group to a single fixed fiducial state. In this paper, we consider metrology with 2-photon ("biphoton") states, and report experimental studies of different states' sensitivity to small, unknown collective SU(2) rotations ("SU(2) jitter"). Maximally entangled N00N states are the most sensitive detectors of such a rotation, yet they are also among the worst at fully characterizing an a-priori unknown process. We identify (and confirm experimentally) the best SU(2)-covariant set for process tomography; these states are all less entangled than the N00N state, and are characterized by the fact that they form a 2-design.