One strategy to the discrimination problem is to identify the state with certainty, leaving a possibility of undecidability. This paper gives an upper bound for the maximal success probability of unambiguous discrimination among n states. This bound coincides with the known IDP limit when two states are considered.
Quantum state separation is a more general operation for identifying states than unambiguous discrimination. In this paper, we derive an upper bound on the success probability of separation among n states with arbitrary a priori probabilities, extending some of the important results given in the literature. This conclusion generalizes that obtained by Chefles and Barnett for separating two states having equal a priori probabilities. Some of the known bounds on the success probabilities of unambiguous discrimination such as the Ivanovic–Dieks–Peres limit, the more general limit by Jaeger and Shimony, and an upper bound for the case of unambiguously discriminating n states, are special cases of our results. Notably, we also give implicitly a different method to derive the upper bound on the probability of successful unambiguous discrimination among n states. Finally, we apply our conclusion to quantum cloning and then derive some upper bounds on the success probabilities for several probabilistic cloning machines.
Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider a revised unambiguous discrimination of quantum resources. First, we present an upper bound of the success probability for a revised unambiguous discrimination task in the unasymptotic and asymptotic scenarios. Next, we generalize the task from quantum states to quantum channels. We present an upper bound of the success probability for the task under the adaptive strategy. Furthermore, we show the bound can be computed efficiently. Finally, compared with the classical unambiguous discrimination, we show the advantage of the quantum by considering a quantifier on a set of semidefinite positive operators.
In this paper, we present a general upper bound on the success probability for unambiguous discrimination among arbitrary m mixed quantum states with given a priori probability. We further analyze how this upper bound can be achievable by presenting a sufficient condition related to it, and we compare this upper bound with three other upper bounds. Moreover, for the issue of the unambiguous identification of m unknown multicopy qudit pure states, we also get a bound.
Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider an extended unambiguous discrimination of quantum resources. First, we present an upper bound of the success probability for an extended unambiguous discrimination task in the non-asymptotic and asymptotic scenarios. Next, we generalize the task from quantum states to quantum channels. We present an upper bound of the success probability for the task under the adaptive strategy. Furthermore, we show the bound can be computed efficiently. Finally, compared with the classical generalized unambiguous discrimination, we show the advantage of the quantum with the aid of a quantifier based on a set of semi-definite positive operators.