Coherence-gated quantum devices via real-time weak measurement

TL;DR

This paper introduces a coherence-gated quantum routing method using real-time weak measurements to enhance quantum information processing and security applications.

Contribution

It proposes a novel coherence-based routing primitive with real-time weak measurement estimation, enabling secure quantum randomness and entanglement certification.

Findings

Coherence score threshold controls photon acceptance.

Benchmarking reveals detector efficiency underestimation stabilizes results.

Purity underestimation can significantly overestimate coherence.

Abstract

Single-photon routers in cavity and circuit QED direct photons by the qubit's energy eigenstate -- a projective decision that destroys coherence. We propose a different primitive: coherence-gated routing, where the decision depends on the magnitude of the qubit's quantum coherence, estimated in real time from simultaneous weak measurements of $\sigma_x$ and $\sigma_z$. A photon is accepted if the coherence score $S(T) = \sqrt{\langle\sigma_x\rangle_c^2 + \langle\sigma_y\rangle_c^2}$, extracted from the conditional density matrix via the stochastic master equation, exceeds a tunable threshold $S_{\mathrm{th}}$. Certifying coherence at emission enables two applications conventional heralded sources cannot: (i) a quantum random number generator with min-entropy bounded by Bloch-sphere geometry, $H_\infty \geq -\log_2\!\bigl(\frac{1+\sqrt{1-S_{\mathrm{th}}^2}}{2}\bigr)$, and (ii) a phase-tracked photon source whose two-node coherence certification bounds the matter--matter entanglement fidelity after Bell-state measurement. The estimator is itself a security primitive. Benchmarking seven configurations, we find that underestimating detector efficiency ($\eta_{\mathrm{a}} < \eta_{\mathrm{true}}$) both stabilizes the numerics and suppresses overcertification. We trace this via a purity-monotonicity result, identify a geometric loophole amplifying purity undercertification into coherence overcertification by an order of magnitude ($\sim$12$\times$), and prove two complementary tail bounds: an Ornstein--Uhlenbeck comparison giving $9.0\%$ overcertification (empirical $6.3\%$ from $10^6$ trajectories) and an exponential supermartingale establishing structural exponential decay.