Abstract
Abstract Discrimination between two quantum states is addressed as a quantum detection process where a measurement with two outcomes is performed and a conclusive binary decision results about the state. The performance is assessed by the overall probability of decision error. Based on the theory of quantum detection, the optimal measurement and its performance are exhibited in general conditions. An application is realized on the qubit, for which generic models of quantum noise can be investigated for their impact on state discrimination from a noisy qubit. The quantum noise acts through random application of Pauli operators on the qubit prior to its measurement. For discrimination from a noisy qubit, various situations are exhibited where reinforcement of the action of the quantum noise can be associated with enhanced performance. Such implications of the quantum noise are analyzed and interpreted in relation to stochastic resonance and enhancement by noise in information processing.
Highlights
Quantum states naturally arise when one wants to process, store or retrieve information at the level of quantum objects, such as individual photons, electrons, ions or atoms
Based on the theory of quantum detection, we have described a setting for quantum state discrimination through a conclusive binary measurement operating on a noisy qubit
The noise is realized by a quantum noise channel of various types acting on the qubit prior to its measurement
Summary
Quantum states naturally arise when one wants to process, store or retrieve information at the level of quantum objects, such as individual photons, electrons, ions or atoms. The type of quantum state discrimination we investigate here, requires a decision about which state the system is in, each time a measurement is performed In this way, quantum state detection here will designate a conclusive discrimination between two alternative quantum states. The probability of error of the optimal detector operating on the noisy qubit will be analyzed in relation to stochastic resonance and enhancement by noise in information processing. Quantum state detection as understood here with no inconclusive measurement, matches the problem of signal detection in the sense of classical (non-quantum) statistical information processing [15,16,49]. Stochastic resonance or enhancement by noise has been shown feasible in classical detection problems [14,15,16,17,18,19]; and it is investigated here for the first time for quantum detection
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