The ability to uniquely identify a quantum state is integral to quantum science, but for nonorthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the nondeterministic protocol of unambiguous state discrimination enables the error-free differentiation of states, at the cost of a lower frequency of success. We discriminate experimentally between nonorthogonal, high-dimensional states encoded in single photons; our results range from dimension d=2 to d=14. We quantify the performance of our method by comparing the total measured error rate to the theoretical rate predicted by minimum-error state discrimination. For the chosen states, we find a lower error rate by more than 1 standard deviation for dimensions up to d=12. This method will find immediate application in high-dimensional implementations of quantum information protocols, such as quantum cryptography.
Abstract In this paper we investigate the advanced unambiguous state discrimination (USD) attack that is crucial for quantum key distribution based on phase-coded coherent states. Performing the attack Eve imposes all discriminated states while she can maintain both detection and error rates at Bob’s side. In this work we give the detailed description of the attack and propose the general approach for countermeasures. As the particular case we introduce the so-called ‘mousetrap’ (uninformative) state which allows to decrease the USD probability and preserve high sifted key rate. We also propose some candidates for ‘mousetrap’ states and provide the estimation on the discrimination probability for each of them.
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank
r in a 2
r-dimensional Hilbert space. These reduction theorems also allow us to reduce USD problems to simpler ones for which the solution might be known. As an application, we consider the unambiguous comparison of
n linearly independent pure states with a simple symmetry. Moreover, lower bounds on the optimal failure probability have been derived. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. We also construct the corresponding optimal measurement. With this result, we provide analytical solutions for unambiguously discriminating a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. We however show that examples exist where the bounds cannot be reached. Next, we derive properties on the rank and the spectrum of an optimal USD measurement. This finally leads to a second class of exact solutions. Indeed we present the optimal failure probability as well as the optimal measurement for unambiguously discriminating any pair of geometrically uniform mixed states in four dimensions. This class of problems includes for example the discrimination of both the basis and the bit value mixed states in the BB84 QKD protocol with coherent states.