Mutual Information and Quantum Discord in Quantum State Discrimination with a Fixed Rate of Inconclusive Outcomes

Abstract

We studied the mutual information and quantum discord that Alice and Bob share when Bob implements a discrimination with a fixed rate of inconclusive outcomes (FRIO) onto two pure non-orthogonal quantum states, generated with arbitrary a priori probabilities. FRIO discrimination interpolates between minimum error (ME) and unambiguous state discrimination (UD). ME and UD are well known discrimination protocols with several applications in quantum information theory. FRIO discrimination provides a more general framework where the discrimination process together with its applications can be studied. In this setting, we compared the performance of optimum probability of discrimination, mutual information, and quantum discord. We found that the accessible information is obtained when Bob implements the ME strategy. The most (least) efficient discrimination scheme is ME (UD), from the point of view of correlations that are lost in the initial state and remain in the final state, after Bob’s measurement.

Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy

“…A notable feature of our experimental setup is that it can be easily configured to implement the optimal FRIO POVM for all pairs of non-orthogonal states, arbitrary a priori probabilities, and any value of the fixed rate of inconclusive outcome. In particular, it allows us to implement MED, UD, and any intermediate case of FRIO by fixing the rate of inconclusive outcomes, showing a good agreement with the theoretical results 53,59 . This experimental platform gives a flexible and customizable toolbox for a wide range of QSD strategies involving the FRIO scheme, which can be helpful to explore novel applications for quantum information protocols and further research in quantum foundations.…”

“…The FRIO solution identifies three intervals where the optimal probabilities can be obtained. These intervals depend on the values of the overlap s and the probability η 1 given a fixed value of Q 53,59 . Interval I is defined as…”

“…This task plays a fundamental role in several remarkable quantum protocols such as quantum key distribution 10 , quantum teleportation 11,12 , entanglement swapping 13,14 , and entanglement concentration 15,16 . Moreover, being a fundamental protocol, QSD also has been studied in relation with: contextuality 17 , path distinguishability [18][19][20] , and quantum correlations [21][22][23] . Thus, there are well-known strategies to implement QSD, namely the minimum error discrimination (MED) 24,25 , the unambiguous discrimination (UD) [26][27][28][29] , and the maximum confidence discrimination (MCD) [30][31][32] , each focused on optimizing some figure of merit 33 .…”

“…In the case of QSD by FRIO, the average error probability in the identification of the quantum state ρ i is minimized under the condition of fixing the probability of inconclusive results 57 . Although for MED, UD and MCD there is no analytical solution to the discrimination by FRIO of N arbitrary non-orthogonal states 58 , in the case of two pure non-orthogonal states with arbitrary a priori preparation probabilities, the complete optimal solution is known 53,59 . Moreover, experimental schemes for the realization of FRIO onto two pure non-orthogonal states have been proposed 60,61 .…”

Unambiguous State Discrimination with Intrinsic Coherence

“…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 ].…”