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Register a new userUnambiguous discrimination of coherent states
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Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are a prime candidate as information carriers for optical communications. A large body of literature exists on quantum-limited parameter estimation and discrimination for coherent states. However, very little is known about practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and establish a theory of unambiguous discrimination of coherent states, with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, un-excited auxiliary input modes, and on-off photon detection. Our results indicate that these currently-available optical components are near optimal for unambiguous discrimination of multiple coherent states in a constellation.
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Generalized quantum measurements identifying non-orthogonal states without ambiguity often play an indispensable role in various quantum applications. For such unambiguous state discrimination scenario, we have a finite probability of obtaining inconclusive results and minimizing the probability of inconclusive results is of particular importance. In this paper, we experimentally demonstrate an adaptive generalized measurement that can unambiguously discriminate the quaternary phase-shift-keying coherent states with a near-optimal performance. Our scheme is composed of displacement operations, single photon detections and adaptive control of the displacements dependent on a history of photon detection outcomes. Our experimental results show a clear improvement of both a probability of conclusive results and a ratio of erroneous decision caused by unavoidable experimental imperfections over conventional static generalized measurements.
We propose an oversimplified scheme to unambiguously discriminate nonorthogonal quantum field states inside high-Q cavities. Our scheme, which is based on positive operator-valued mea- sures (POVM) technique, uses a single three-level atom interacting resonantly with a single mode of a cavity-field and selective atomic state detectors. While the single three-level atom takes the role of the ancilla, the single cavity mode field represents the system we want to obtain information. The efficiency of our proposal is analyzed considering the nowadays achievements in the context of cavity QED.
In this work we propose the technique for phase-coded weak coherent states protocols utilizing two signal states and one decoy state which is found as linear combination of signal states (Schrodinger Cat states); the latter allows to overcome the USD attack. For instance, Schrodinger Cat states can be considered as even coherent states. Moreover we consider decoy states implementation based on squeezed vacuum states which might not disables USD completely yet produces discrimination probabilities low enough to distribute keys in channel with particular losses. Thus we can detect Eve simply by monitoring the detection rate of decoy states. It should be noted that this approach can be scaled to more complex schemes.
The optimal discrimination of non-orthogonal quantum states with minimum error probability is a fundamental task in quantum measurement theory as well as an important primitive in optical communication. In this work, we propose and experimentally realize a new and simple quantum measurement strategy capable of discriminating two coherent states with smaller error probabilities than can be obtained using the standard measurement devices; the Kennedy receiver and the homodyne receiver.
Optimization of the mean efficiency for unambiguous (or error free)discrimination among $N$ given linearly independent nonorthogonal states should be realized in a way to keep the probabilistic quantum mechanical interpretation. This imposes a condition on a certain matrix to be positive semidefinite. We reformulated this condition in such a way that the conditioned optimization problem for the mean efficiency was reduced to finding an unconditioned maximum of a function defined on a unit $N$-sphere for equiprobable states and on an $N$-ellipsoid if the states are given with different probabilities. We established that for equiprobable states a point on the sphere with equal values of Cartesian coordinates, which we call symmetric point, plays a special role. Sufficient conditions for a vector set are formulated for which the mean efficiency for equiprobable states takes its maximal value at the symmetric point. This set, in particular, includes previously studied symmetric states. A subset of symmetric states, for which the optimal measurement corresponds to a POVM requiring a one-dimensional ancilla space is constructed. We presented our constructions of a POVM suitable for the ancilla space dimension varying from 1 till $N$ and the Neumarks extension differing from the existing schemes by the property that it is straightforwardly applicable to the case when it is desirable to present the whole space system + ancilla as the tensor product of a two-dimensional ancilla space and the $N$-dimensional system space.
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