Quantum

Quantum-Assisted Unambiguous Discrimination of Pure States with Robustness Bounds

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Briefings

A hybrid quantum-classical framework using the NSS solver and reciprocal-state representation enables unambiguous discrimination of pure states. The method reduces optimization variables from the full Gram matrix to N scalar variables (where N is the number of states) and introduces robustness guarantees against Gram matrix estimation errors via a rescaling procedure. Numerical simulations validate these bounds, and experiments on IBM hardware estimate pairwise overlaps to evaluate resulting POVMs.

Key points

• The framework combines the noisy intermediate-scale quantum semidefinite program solver (NSS) with the reciprocal-state representation to solve discrimination problems for circuit-prepared states.
• The method reduces the number of optimization variables and positive-semidefinite constraints compared to the original NSS formulation by choosing discriminated states as ansatz states and exploiting the reciprocal-state representation.

Context

This research proposes a new approach to quantum state discrimination that leverages hybrid quantum-classical computation to improve efficiency and robustness against measurement noise.

Limitations

Robustness bounds are established using estimated Gram matrices and perturbation bounds rather than the ideal Gram matrix; numerical simulations and IBM hardware experiments validate the framework but do not constitute definitive proof of performance in real-world conditions.

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