Random access Bell game by sequentially measuring the control of the quantum SWITCH

Abstract

Preserving quantum correlations such as Bell nonlocality in noisy environments remains a fundamental challenge for quantum technologies. We introduce the Random Access Bell Game (RABG), a task where an entangled particle propagates through a sequence of identical noisy blocks, and the ability to violate a Bell inequality is tested at a randomly chosen point (access node). We consider a scenario where each noisy block is composed of two complete erasure channels, an extreme entanglement-breaking channel with vanishing quantum and classical capacities. We investigate the performance of the Random Access Bell Game in this configuration and attempt to mitigate the effect of noise by coherently controlling the order of each channel in the noise using the quantum {\tt SWITCH}. However, the quantum {\tt SWITCH} in its canonical setup with a coherent state in the control fails to provide any advantage in the Random Access Bell Game. Our main contribution is a protocol that leverages initial entanglement between the target and control of the quantum {\tt SWITCH} and employs sequential, unsharp measurements on the control system, showing that it is possible to guarantee a Bell violation after an arbitrarily large number of channel applications. Furthermore, our protocol allows for a near-maximal (Tsirelson bound) Bell violation to be achieved at any desired round, while still ensuring violations in all preceding rounds. We prove that this advantage is specific to generalized Greenberger-Horne-Zeilinger (GHZ) states, as the protocol fails for W-class states, thus providing an operational way to distinguish between these two fundamental classes of multipartite entanglement.

Figures (3)

• Figure 1: Schematic of the random access Bell game. The subsystem at B repeatedly passes through identical noise blocks. The particle can be picked randomly from any access nodes and used to assess the Bell violation.
• Figure 2: Random Access Bell Game using the quantum SWITCH. The initial state $\rho_{CAB_0}$ is passed through the coherently controlled noise, e.g., the SWITCH action, with C acting as the control. A measurement is then performed at C and the outcomes are communicated to Alice and Bob.
• Figure 3: Persistence of Bell Violation. Maximum rounds of violation $N_{\max}(|\mathcal{B}_{\min}|, \alpha)$ (ordinate) with respect to violation threshold $|\mathcal{B}_{\min}|$. The $N_{\max}$ value approaches $\infty$ as the threshold $|\mathcal{B}_{\min}|$ approaches 2, as predicted by our analysis. All axes are dimensionless.

Theorems & Definitions (18)

• Lemma 1
• proof
• Lemma 2
• proof
• proof
• Theorem 1
• proof
• Corollary 1
• Theorem 2
• proof