Characterization of high-dimensional entangled systems via mutually unbiased measurements

TL;DR

This paper demonstrates an efficient method for quantum state reconstruction of high-dimensional entangled systems by using mutually unbiased measurements on individual subsystems, simplifying the process compared to defining MUBs for the entire system.

Contribution

The authors experimentally show that measuring MUBs on subsystems enables quantum state reconstruction of high-dimensional entangled states, avoiding the complexity of defining MUBs for the whole system.

Findings

Successful state reconstruction for dimensions 2 to 5.

Measurement of MUBs on subsystems simplifies high-dimensional state analysis.

Applicable to entangled photons in orbital angular momentum states.

Abstract

Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multi-partite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum (OAM) degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d=2 to 5.