Unambiguous quantum state discrimination (UQSD), assisted by an auxiliary system, generally requires quantum correlations as a resource. We find that quantum coherence can be utilized as a resource in an allied UQSD protocol that is devoid of quantum correlations. We propose a mechanism for quantum state discrimination where the non-orthogonality of the input states can be converted to quantum coherence of the auxiliary system. We quantify the required coherence generated during this and the optimal unambiguous quantum state discrimination strategy in some specific cases. In particular, our result introduces how to find the optimal strategy by measuring quantum coherence in protocols that discriminates between two non-orthogonal quantum states.
Unambiguous quantum state discrimination (UQSD), assisted by an auxiliary system, generally requires quantum correlations as a resource. We find that quantum coherence can be utilized as a resource in an allied UQSD protocol that is devoid of quantum correlations. We propose a mechanism for quantum state discrimination where the non-orthogonality of the input states can be converted to quantum coherence of the auxiliary system. We quantify the required coherence generated during this and the optimal unambiguous quantum state discrimination strategy in some specific cases. In particular, our result introduces how to find the optimal strategy by measuring quantum coherence in protocols that discriminates between two non-orthogonal quantum states.
Unambiguous quantum state discrimination (UQSD), assisted by an auxiliary system, generally requires quantum correlations as a resource. We find that quantum coherence can be utilized as a resource in an allied UQSD protocol that is devoid of quantum correlations. We propose a mechanism for quantum state discrimination where the non-orthogonality of the input states can be converted to quantum coherence of the auxiliary system. We quantify the required coherence generated during this and the optimal unambiguous quantum state discrimination strategy in some specific cases. In particular, our result introduces how to find the optimal strategy by measuring quantum coherence in protocols that discriminates between two non-orthogonal quantum states.
Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.
The roles of quantum correlations, entanglement, discord, and dissonance needed for performing unambiguous quantum state discrimination assisted by an auxiliary system are studied. In general, this procedure for conclusive recognition between two nonorthogonal states relies on the availability of entanglement and discord. However, we find that there exist special cases for which the procedure can be successfully achieved without entanglement. In particular, we show that the optimal case for discriminating between two nonorthogonal states prepared with equal a priori probabilities does not require entanglement but quantum dissonance only.
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 discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here we consider a variant of that problem; rather than discriminating among all of the different states, we shall discriminate between two subsets of them. In particular, for the case of 3 states, we find the optimal strategy to distinguish one from the other two. This procedure has a higher probability of success than distinguishing all 3 states. We show how to construct generalized interferometers that provide an implementation of the optimal strategy.
The discrimination of two mixed quantum states is a fundamental task in quantum state estimation and quantum information theory. In quantum state discrimination a quantum system is assumed to be in one of two possible – in general mixed – non-orthogonal quantum states. The discrimination then consists of a measurement strategy that allows to decide in which state the system was before the measurement. In unambiguous state discrimination the aim is to make this decision without errors, but it is allowed to give an inconclusive answer.
Especially interesting are measurement strategies that minimize the probability of an inconclusive answer. A starting point for the analysis of this optimization problem was a result by Eldar et al. [Phys. Rev. A 69, 062318 (2004)], which provides non-operational necessary and sufficient conditions for a given measurement strategy to be optimal. These conditions are reconsidered and simplified in such a way that they become operational. The simplified conditions are the basis for further central results: It is shown that the optimal measurement strategy is unique, a statement that is e.g. of importance for the complexity analysis of optimal measurement devices. The optimal measurement strategy is derived for the case, where one of the possible input states has at most rank two, which was an open problem for many years. Furthermore, using the optimality criterion it is shown that there always exists a threshold probability for each state, such that below this probability it is optimal to exclude this state from the discrimination strategy.
If the two states subject to discrimination can be brought to a diagonal structure with (2×2)-dimensional blocks, then the unambiguous discrimination of these states can be reduced to the unambiguous discrimination of pure states.
A criterion is presented that allows to identify the presence of such a structure for two self-adjoint operators. This criterion consists of the evaluation of three commutators and allows an explicit construction of the (2×2)-dimensional blocks.
As an important application of unambiguous state discrimination, unambiguous
state comparison, i.e., the question whether two states are identical or not, is generalized and optimal measurements for this problem are constructed.
If for a certain family of states, a physical device maps the input state to an output state, such that a second device can be built that yields back the original input state, such a map is called reversible on this family. With respect to state discrimination, such reversible maps are particularly interesting, if the output states are pure. A complete characterization of all families that allow such a reversible and purifying map is provided. If the states are mapped to pure states, but the map itself is not reversible, upper and lower bounds are analyzed for the “deviation from perfect faithfulness”, a quantity which measures the deviation from a reversible mapping.