Maximal LELM Distinguishability of Qubit and Qutrit Bell States Using Projective and Non-Projective Measurements

TL;DR

This paper investigates the limits of distinguishing Bell states in qubits and qutrits using projective and non-projective measurements, revealing fundamental constraints and maximum distinguishability bounds.

Contribution

It establishes the maximum number of Bell states distinguishable via projective and non-projective LELM measurements for qubits and qutrits, extending the no-go theorem.

Findings

Only three of four qubit Bell states can be distinguished with projective LELM.

Maximum of five qutrit Bell states can be distinguished with generalized LELM.

General LELM measurements cannot reliably distinguish all four qubit Bell states.

Abstract

Numerous quantum information protocols make use of maximally entangled two-particle states, or Bell states, in which information is stored in the correlations between the two particles rather than their individual properties. Retrieving information stored in this way means distinguishing between different Bell states, yet the well known no-go theorem establishes that projective linear evolution and local measurement (LELM) detection schemes can only reliably distinguish three of the four qubit Bell states. We establish maximum distinguishability of the qutrit Bell states of bosons via projective LELM measurements; only three of the nine Bell states can be distinguished. Next, we extend to the case of non-projective measurements. We strengthen the no-go theorem by showing that general LELM measurements cannot reliably distinguish all four qubit Bell states. We also establish that at most five qutrit Bell states can be distinguished with generalized LELM measurements.