Universal framework for simultaneous tomography of quantum states and SPAM noise

TL;DR

This paper introduces a universal denoising algorithm for quantum tomography that simultaneously characterizes quantum states and measurement noise, accommodating various prior knowledge and noise correlations.

Contribution

It provides a general framework for joint quantum state and noise tomography that extends existing methods and handles correlated errors without assuming noise invertibility.

Findings

Can fully characterize SPAM errors in quantum systems.

Handles correlated errors and arbitrary states without noise assumptions.

Reduces measurements needed using prior information.

Abstract

We present a general denoising algorithm for performing simultaneous tomography of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.