Quantum state discrimination and enhancement by noise

Joonwoo Bae

Min Namkung, Hyang-Tag Lim

Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit contextuality-enhanced success probabilities that surpass classical bounds, offering significant advantages for quantum sensing and communication. However, in practice, both error and failure outcomes can occur, suggesting the need for a unified strategy that incorporates both aspects while exploring the potential for contextuality enhancement. In this work, we theoretically demonstrate contextuality enhancement in quantum state discrimination under a fixed failure probability. We show that this enhancement disappears within a certain intermediate range of failure probabilities--a phenomenon absent in conventional strategies, where both minimum-error and unambiguous discrimination consistently outperform the noncontextual bound for equal priors. Moreover, we analyze how the existence of this non-enhancement region depends on the confusability of the quantum states, which corresponds to their fidelity in a quantum model. We further extend the discussion to the noisy state discrimination, which even encompasses the maximal-confidence discrimination. In this extended discussion, we observe that the non-enhancement region tends to disappear with increasing noise strength.

Ulrike Futschik

Giovanni Chesi, Stefano Olivares, Matteo G. A. Paris

We address binary phase-shift-keyed communication channels based on Gaussian states and prove that squeezing improves state discrimination at fixed energy of the channel, and also in the presence of phase diffusion. We then assess performances of homodyne detection against the ultimate quantum limits to discrimination and show that homodyning achieves optimality in the large-noise regime. Finally, we consider noise in the preparation of the seed signal (before phase encoding) and show that, also in this case, squeezing may improve state discrimination in realistic conditions.

Andrew R. Ferdinand, M. T. DiMario, F. E. Becerra

Abstract Measurements approaching the ultimate quantum limits of sensitivity are central in quantum information processing, quantum metrology, and communication. Quantum measurements to discriminate multiple states at the single-photon level are essential for optimizing information transfer in low-power optical communications and quantum communications, and can enhance the capabilities of many quantum information protocols. Here, we theoretically investigate and experimentally demonstrate the discrimination of multiple coherent states of light with sensitivities surpassing the quantum noise limit (QNL) at the single-photon level under realistic conditions of loss and noise based on strategies implementing globally-optimized adaptive measurements with single photon counting and displacement operations. These discrimination strategies can provide realistic advantages to enhance information transfer at low powers, and are compatible with photon number resolving detection, which provides robustness at high powers, thus allowing for surpassing the QNL at arbitrary input power levels under realistic conditions.

Elif Cüce, Saeed A. Khan, Boris Mesits +2 more

Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio, an objective that is well-suited to parameter estimation but is typically insufficient for more general tasks such as arbitrary quantum state discrimination. Here we show that single-shot quantum state classification can benefit from operating a quantum amplifier outside the linear regime, when the measurement chain is optimized end-to-end for a task-specific cost function. We analyze a realistic superconducting readout architecture that includes state preparation, cryogenic nonlinear amplification, and room-temperature detection with finite noise. By introducing performance metrics tailored to state discrimination, we identify operating regimes in which nonlinear amplification provides a measurable advantage and clarify the trade-offs that ultimately limit classification fidelity. Building on these results, we propose a qubit readout architecture without cavity displacement that exploits nonlinear amplification to enhance single-shot state discrimination performance. Our results establish the practical value of nonlinear quantum amplifiers for quantum state discrimination and lay the foundation for a broader program to develop a general, end-to-end framework for resource-constrained optimization of nonlinear amplification in quantum information processing tasks.