Reliable Quantum State Tomography

TL;DR

This paper introduces a method for quantum state tomography that provides reliable, operationally meaningful error bounds in the form of confidence regions, applicable to various measurements and especially practical for small quantum systems.

Contribution

It develops a data analysis procedure that yields tight confidence regions for quantum states, ensuring high-probability accuracy without prior assumptions, applicable to arbitrary measurements.

Findings

Provides a practical method for confidence regions in quantum tomography.

Applicable to all measurement types, including coherent measurements.

Effective for small quantum systems like few-qubit states.

Abstract

Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic limits, the estimates computed by standard methods do not in general coincide with the true state, and therefore have no operational significance unless their accuracy is defined in terms of error bounds. Here we show that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions - a concept originating from classical statistics. Confidence regions are subsets of the state space in which the true state lies with high probability, independently of any prior assumption on the distribution of the possible states. Our method for computing confidence regions can be applied to arbitrary measurements including fully coherent ones; it is practical and particularly well suited for tomography on systems consisting of a small number of qubits, which are currently in the focus of interest in experimental quantum information science.