Quantum state estimation when qubits are lost: A no-data-left-behind approach

TL;DR

This paper introduces a Bayesian quantum state estimation method that effectively utilizes all available data, including lost qubits, providing a practical approach for complex quantum experiments.

Contribution

It presents a novel hyperspherical parametrization and likelihood approach enabling Bayesian estimation with complete data usage, applicable to any quantum state dimension.

Findings

First closed-form Bayesian estimate for a single qubit

Numerical sampling applied to a two-qubit photonic experiment

Reduces computational burdens from experimental asymmetries

Abstract

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean estimate for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.