Optimal linear optical discrimination of Bell-like states

TL;DR

This paper investigates the limits of linear optical systems in unambiguously discriminating Bell-like quantum states without ancillary photons, revealing a lower success probability than for true Bell states and proposing an optimal configuration.

Contribution

It demonstrates that the optimal success probability for Bell-like states is 25%, lower than the 50% for Bell states, and provides a specific linear optical setup for optimal discrimination.

Findings

Optimal success probability for Bell-like states is 25%.

Proposed a linear optical configuration for optimal discrimination.

Compared distinguishability and entanglement of Bell-like states.

Abstract

Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillas, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50% we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprised of single photon detectors and beam splitters with input state-dependent parameters that achieves optimal discrimination in the Bell-like case.