Symmetric joint measurement as a complement to the elegant joint measurement

TL;DR

This paper introduces a new symmetric joint measurement for two-qubit systems, expanding the set of measurement bases with unique symmetry properties and applications in quantum networks, complementing existing measurements like the elegant joint measurement.

Contribution

It presents a novel symmetric joint measurement with variable concurrence, explores its symmetry properties, and generalizes it to multiqubit systems, filling a gap between known measurement bases.

Findings

The new measurement has concurrence from 0 to 1/2.

It exhibits rotational symmetry in its reduction vectors.

Output distributions show permutation symmetry in networks.

Abstract

Traditional Bell state measurement (BSM) and product basis measurements (PBM) have been integral to nearly the entire development of quantum computing. Unlike the BSM and the PBM, a recently proposed two-qubit joint measurement called the elegant joint measurement (EJM) exhibits novel tetrahedral symmetry in its single-qubit reduced states. In [Phys.Rev.Lett.126:220401], a parameterized two-qubit iso-entangled basis was proposed, with concurrence between 1/2 and 1, perfectly spanning the original EJM and conventional BSM. We present a two-qubit symmetric joint measurement having concurrence from 0 to 1/2, which is complementary to [Phys.Rev.Lett.126:220401] and contains the PBM and the original EJM. We investigate the symmetry of the current structure and its application in triangular networks. The results indicate that the reduction vectors of the current basis states exhibit rotational symmetry, rather than the aforementioned mirror symmetry; moreover, the output probability distributions of three parties in the network explicitly demonstrate the expected permutation symmetry. Furthermore, we generalize the two-qubit symmetric joint measurement to the multiqubit systems with an even number of qubits.