Estimation of pure states using three measurement bases

TL;DR

This paper presents a novel method for estimating unknown pure quantum states in high dimensions using only three measurement bases, validated through experiments on photonic and superconducting platforms.

Contribution

The paper introduces a new measurement-based protocol for pure state estimation using only three bases, applicable to high-dimensional quantum systems.

Findings

Successfully estimated 8-dimensional pure states with high accuracy.

Demonstrated the method's effectiveness on a superconducting qubit processor.

Validated the protocol on two different quantum platforms.

Abstract

We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of $2^{d-1}$ possible states, the likelihood of which is evaluated using the measurement results of the $d$ remaining projectors. The state with the highest likelihood is the estimate of the unknown state. The method estimates all pure states but a null-measure set. The viability of the protocol is experimentally demonstrated using two different and complementary high-dimensional quantum information platforms. First, by exploring the photonic path-encoding strategy, we validate the method on a single 8-dimensional quantum system. Then, we resort to the five superconducting qubit IBM quantum processor to demonstrate the high performance of the method in the multipartite scenario.