Minimum-error discrimination between two sets of similarity-transformed quantum states

Jafarizadeh, M. A.; Khiavi, Y. Mazhari; Kourbolagh, Y. Akbari

doi:10.48550/arxiv.1106.5883

Cited by 1 publication

(1 citation statement)

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“…In the general case of N = 3 states, the minimum error discrimination solution for pure qubit states was obtained in [17,18]. The analytic solution for mixed qubit states without necessary and sufficient conditions was obtained in [19], and the complete analysis was performed in [20]. Unambiguous state discrimination can be achieved only for linearly independent states [21], and therefore is not possible for N = 3 qubit states.…”

Section: Introductionmentioning

confidence: 99%

PT-symmetric distinction of three states and its implementation on a cloud quantum processor

Balytskyi

Kotukh

Khalimov³

et al. 2022

Preprint

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We present a novel $\mathcal{PT}$-symmetric approach for discriminating three pure qubit states and its implementation by the dilation method. Our approach based on the dilation method manipulating the Hilbert space of the system by two-staged $\mathcal{PT}$-symmetric evolution expedites the three-state discrimination process at the cost of introducing an inconclusive outcome. This modification of the Hilbert space of the qubit makes it possible to eliminate one of three states in the limit $\alpha\rightarrow\pm\frac{\pi}{2}$ in the vicinity of the exceptional point corresponding to coalescing eigenvectors and eigenvalues, effectively reducing the problem to two-state discrimination, or reducing the geometry to the mirror-symmetric states for which an efficient discrimination strategy is developed. To demonstrate the effectiveness of our approach, we implement it on a superconducting quantum processor provided by IBM Quantum Experience employing an ancilla qubit. We conclude our paper by identifying potential applications, including those in quantum communication and cryptography, to facilitate further research and development.

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