Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution

Abstract

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

Unambiguous State Discrimination with Intrinsic Coherence

“…Sequential state discrimination (SSD) provided in [ 13 ] is a scheme for discriminating one sender’s quantum states via N observers who are separately located. SSD is investigated sequentially in [ 16 , 17 , 22 , 41 ]. As a next step, we plan to investigate another interesting problem corresponding to SSD including quantum filtering and rank- N mixed states discriminations and consider the role played by quantum correlation and coherence in the procedure.…”

Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

“…Next, the sender sends the state to the receiver, and the receiver determines what the state is. In the state discrimination, there are many strategies such as minimum error discrimination (MED) [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ], unambiguous discrimination [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ], discrimination with a fixed error [ 24 , 25 , 26 , 27 ] etc. In particular, the MED is the optimal measurement strategy that minimizes the average error probability.…”