Contextuality of quantum non-demolition measurement via state discrimination

Abstract

Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model--referred to as a noncontextual model--making it crucial to identify which features prevents such models from reproducing the corresponding quantum measurements. In this work, we theoretically demonstrate contextual features inherent in the structure of quantum non-demolition measurements. These features not only reveal the nonclassicality of unambiguous state discrimination, but also extend to sequential unambiguous discrimination and probabilistic quantum cloning, both of which involve post-measurement states. Moreover, our analysis extends to noisy scenarios, highlighting its potential relevance for practical implementations. We believe that our results broaden the scope of observing nonclassicality in quantum systems and ultimately contribute to the advancement of various quantum technologies.

Figures (5)

• Figure 1: Structure of non-demolition measurement. (a) Structure in the quantum model, consisting of an auxiliary state $|\psi_{\rm aux}\rangle$, a unitary operator $\hat{U}$, and a direct measurement ${\hat{\Pi}_k}$. The post-measurement state is denoted by $|\widetilde{\psi}_k\rangle$. (b) Structure in a noncontextual ontological model, consisting of a transformation $\mathcal{L}$ and a direct measurement ${\pi_k(\lambda_{{\rm A}}')}$, yielding the post-measurement epistemic state $\widetilde{\mu}_k(\lambda_{{\rm S}}')$.
• Figure 2: Non-demolition measurement reproduced within the noncontextual model for performing unambiguous discrimination between two epistemic states $\mu_1(\lambda_{\rm S})$ and $\mu_2(\lambda_{\rm S})$.
• Figure 3: Non-demolition measurement reproduced within the noncontextual model for sequential unambiguous discrimination between two epistemic states $\mu_1(\lambda_{\rm S})$ and $\mu_2(\lambda_{\rm S})$, performed by two consecutive receivers.
• Figure 4: Non-demolition measurement reproduced within the noncontextual model for probabilistic quantum cloning. (a) Type-I probabilistic quantum cloning, in which two epistemic states are also unambiguously discriminated. (b) Type-II probabilistic quantum cloning, in which only quantum cloning is performed with a certain probability.
• Figure 5: Proposed experimental setup for unambiguous (maximal-confidence) discrimination between two arbitrary polarized single-photon states in the absence (presence) of a depolarizing channel y.-c.jeong. The HWP($\varphi$) is configured according to the prior probabilities of the two states. A displaced Sagnac interferometer, consisting of a PBS, HWP($\mu$), and HWP($\nu$), directs the photon to path $p_0$ with a certain probability, corresponding to a failure outcome. Otherwise, the photon is routed to path $p_1$ or $p_2$, corresponding to outcomes $j=1$ and $j=2$, respectively (PBS: polarizing beam splitter; HWP: half-wave plate).