Discriminating bipartite mixed states by local operations

Abstract

Unambiguous state discrimination of two mixed bipartite states via local operations and classical communications (LOCC) is studied and compared with the result of a scheme realized via global measurement. We show that the success probability of a global scheme for mixed-state discrimination can be achieved perfectly by the local scheme. In addition, we simulate this discrimination via a pair of pure entangled bipartite states. This simulation is perfect for local rather than global schemes due to the existence of entanglement and global coherence in the pure states. We also prove that LOCC protocol and the sequential state discrimination (SSD) can be interpreted in a unified view. We then hybridize the LOCC protocol with three protocols (SSD, reproducing and broadcasting) relying on classical communications. Such hybridizations extend the gaps between the optimal success probability of global and local schemes, which can be eliminated only for the SSD rather than the other two protocols.

Unambiguous State Discrimination with Intrinsic Coherence

“…To see the essential difference between quantum superposition and classical mixture, and the role played by quantum coherence in high-dimensional mixed state discrimination, we replace the classical probability with quantum probability amplitudes. Then, the vectors ( ) in the decomposition of are superposed into a pure state [ 22 ], where .…”

“…The conditions in Equation ( 31 ) also ensure that the discrimination of and can be carried out in N independent subspaces through optimal POVM operators which can be written as a direct sum of N corresponding parts, just like the results for the discrimination of rank-two mixed state in [ 14 , 22 ]. Then, concerning the optimal discrimination of and , we have the following remark.…”

“…We have the following theorem as an extension of the work for the discriminating rank-two mixed states in [ 22 ].…”

“…While the unambiguous quantum state discrimination is error-free [ 7 , 8 , 9 , 10 , 11 , 12 ]. It plays key roles in various contexts in quantum information theory, including quantum key distribution [ 11 , 13 , 16 ], the study of quantum correlations [ 18 , 19 , 20 , 21 ], and the role of entanglement in local discrimination of bipartite systems [ 22 ].…”

“…If the fidelity of the pure-pure state equals the pure-mixed one, it can be proved that the pure-pure scheme is superior to the pure-mixed one; but the coherence is detrimental to the state discrimination for lower dimensional systems. Furthermore, through the discrimination of two rank- N mixed states and the comparison with the results of another pure-pure-state discrimination scheme, as an extension of the results in [ 22 ], we prove that pure-pure scheme is still superior to mixed-mixed one if the eigenvectors of the mixed states have a one-to-one overlap (an equal-fidelity case); but there exists a great deal of symmetrically distributed coherence which is helpful to state discrimination, in contrary to the result of quantum filtering.…”