Optimal nonlocal conversion of photonic four-partite entanglement from two Bell pairs in quantum networks

TL;DR

This paper investigates optimal and practical methods for converting two Bell pairs into four-qubit entangled states in optical quantum networks, focusing on success probabilities and resource efficiency.

Contribution

It introduces necessary and sufficient conditions for state conversion without ancillary qubits and analyzes success probabilities in passive linear optical systems with and without ancillary qubits.

Findings

Derived conditions for nonlocal state conversion without ancillas

Established upper bounds on success probabilities in linear optical systems

Compared optimal success rates with previous schemes

Abstract

We analyze optimal schemes and also propose some practical schemes for the nonlocal conversion from two shared Bell pairs to four-qubit entangled states in optical quantum networks. In the analysis, we consider two-qubit operations as nonlocal operations and minimize the number of access to ancillary qubits as possible. First, we consider two-qubit unitary operations without using ancillary qubits and derive a necessary and sufficient condition for convertible states. Second, we consider nonlocal optical systems composed of passive linear optics and postselection. For the passive linear optical systems, we derive achievable upper bounds of success probabilities of the conversion in the case without ancillary qubits. We also compare the optimal success probabilities with those of previously proposed schemes. Finally, we discuss success probabilities of the conversion in the case with ancillary qubits.