Quantum State Conclusion?

Mei-Yu Wang, Fengli Yan

In this paper, we have considered the problem of general conclusive quantum state classification; the necessary and sufficient conditions for the existence of conclusive classification strategies have also been presented. Moreover, we have given the upper bound for the maximal success probability.

David S. Simon

Elena R. Loubenets, M. Namkung

In the present paper, we develop a general mathematical framework for discrimination between $$r\geq2$$ quantum states by $$N\geq1$$ sequential receivers for the case in which every receiver obtains a conclusive result. This type of discrimination constitutes an $$N$$ -sequential extension of the minimum-error discrimination by one receiver. The developed general framework, which is valid for a conclusive discrimination between any number $$r\geq2$$ of quantum states, pure or mixed, of an arbitrary dimension and any number $$N\geq1$$ of sequential receivers, is based on the notion of a quantum state instrument, and this allows us to derive new important general results. In particular, we find a general condition on $$r\geq2$$ quantum states under which, within the strategy in which all types of receivers’ quantum measurements are allowed, the optimal success probability of the $$N$$ -sequential conclusive discrimination between these $$r\geq2$$ states is equal to that of the first receiver for any number $$N\geq2$$ of further sequential receivers and specify the corresponding optimal protocol. Furthermore, we extend our general framework to include an $$N$$ -sequential conclusive discrimination between $$r\geq2$$ arbitrary quantum states under a noisy communication. As an example, we analyze analytically and numerically a two-sequential conclusive discrimination between two qubit states via depolarizing quantum channels. The derived new general results are important both from the theoretical point of view and for the development of a successful multipartite quantum communication via noisy quantum channels.

Galina Nemova

Yìlè Yīng, David Schmid, Robert W. Spekkens

The task of conclusive exclusion for a set of quantum states is to find a measurement such that for each state in the set, there is an outcome that allows one to conclude with certainty that the state in question was not prepared. Defining classicality of statistics as realizability by a generalized-noncontextual ontological model, we show that there is a quantum-over-classical advantage for how well one can achieve conclusive exclusion. This is achieved in an experimental scenario motivated by the construction appearing in the Pusey-Barrett-Rudolph theorem. We derive noise-robust noncontextuality inequalities bounding the conclusiveness of exclusion, and describe a quantum violation of these. Finally, we show that this bound also constitutes a classical causal compatibility inequality within the bilocality scenario, and that its violation in quantum theory yields a novel possibilistic proof of a quantum-classical gap in that scenario.

Lev Deych