Optimal discrimination of quantum states over a noisy channel

Masashi Ban

Joonwoo Bae

Quantum state discrimination is a fundamental task in quantum information theory and also an important building block in practical quantum information applications. We here consider optimal state discrimination in a noisy environment in which quantum states may be corrupted due to the intervention of an environment. We show that even if there exists an unwanted interaction with an environment and the channel describing the interaction is not yet identified, a measurement prepared in the beginning for optimal state discrimination can be preserved as an optimal measurement ever after a channel use. This means that in a practical realization of quantum communication, verification of a channel can be circumvented and the cost of quantum tomography is saved. We also show a protocol of preserving an optimal measurement for state discrimination.

Satyaki Manna

Among the intriguing features of quantum theory, the problem of distinguishing quantum channels is of fundamental interest. In this paper, we focus on the single-shot discrimination of two noisy quantum channels using two distinct classes of probes: single-system (product) probes and entangled probes. Our aim is to identify optimal probing state for specific discrimination tasks and to analyze the necessity and role of entanglement in enhancing channel distinguishability. We show that maximally entangled probes are optimal for discriminating two qubit depolarizing channels, with any nonzero entanglement providing an advantage over single-system probes. In contrast, for dephasing channels in arbitrary dimensions, we prove that single-system probe can be optimal and that entanglement offers no improvement, even when the dephasing unitary is generalized. For qubit amplitude-damping channels, we identify distinct noise-dependent regimes in which either single-system probe outperforms maximally entangled probes and vice-versa. Moreover, we demonstrate that non-maximally entangled probes can act as the optimum probe if the noise parameters restricted to certain values in this task. We also present examples of noisy unitary channels for which discrimination is possible using non-maximally entangled probe, while both single-systems and maximally entangled probes fail. We introduce another class of noisy unitary channels for which perfect discrimination is achievable with a single system, while maximally entangled probes are insufficient. Finally, we show that two erasure channels can be optimally discriminated using any pure single-system probe, with no advantage gained from entanglement.

François Chapeau‐Blondeau

Miroslav Ježek

Discrimination task is treated in the case of only partial prior information from measurements of unknown quantum sources. The construction of the optimal discrimination device and estimation of quantum states produced by unknown sources is performed simultaneously. A communication through a noisy quantum channel is formulated in terms of the proposed discrimination protocol.

Michael Nussbaum, Arleta Szkoła