Quantum advantage by designing beneficial dissipation from lossless dynamics

Abstract

Passive loss removes probability from a system and therefore seems unable to improve an unconditional target. This intuition is exact for classical population dynamics under sink-only removal: passive killing obeys a finite-strength monotonicity principle even after optimization over the remaining controls. Here we show that coherent quantum dynamics can violate this classical monotonicity because coherent contributions to the final target can interfere destructively. We derive a trajectory-level criterion that determines when such a detrimental contribution is physically accessible to passive loss and accumulates into a net unconditional benefit. The criterion is encoded in a response operator constructed entirely from the lossless dynamics: its spectrum determines whether weak passive loss can help, while its principal eigenvector identifies the optimal environmental mode. Applying this criterion to vibronically assisted transfer, we identify a beneficial mode formed by coherently combining two individually detrimental local loss directions. The predicted mode remains near-optimal at finite loss, producing an \(8.73\%\) enhancement over the independently optimized lossless benchmark, compared with \(9.52\%\) under full finite-loss optimization. Our results establish how coherent quantum dynamics can evade classical passive-loss monotonicity and provide a general task-dependent principle for designing beneficial passive environments from lossless dynamics.

Can irreversible passive loss improve an unconditional quantum target, without postselection or population recycling? The paper contrasts quantum dynamics with classical Markov processes, where sink-only killing cannot increase any nonnegative terminal reward, even after optimizing the remaining controls: $R_{\rm cl}^{\rm opt}(\gamma)\le R_{\rm cl}^{\rm opt}(0)$ for all $\gamma\ge0$. For quantum dynamics, it derives a weak-loss response operator from the lossless forward state $\rho_s$ and backward target effect $E_s$: $G=-(1/T)P_{\rm adm}\int_0^T\{\rho_s,E_s\}/2\,ds\,P_{\rm adm}$. If every positive, trace-normalized loss operator on the admissible subspace is implementable, a positive first-order benefit exists exactly when $\lambda_{\max}(G)>0$; a principal eigenvector specifies the optimal rank-one loss mode. A three-state Bell-target example illustrates why instantaneous signed response must also be physically accessible and accumulate favourably along a fixed mode. Numerical tests use a donor–acceptor vibronic model. A coherent superposition of two individually detrimental local loss directions captures $82.5\%$ of the unrestricted optimal weak-loss response. Fixing this lossless-designed mode and reoptimizing frequency and duration gives an $8.73\%$ finite-loss improvement over the independently optimized lossless benchmark; full environmental reoptimization gives $9.52\%$. Incoherent mixtures remain below that benchmark over the tested interval $0<\gamma/J\le4$. Auxiliary-level simulations verify convergence to the effective loss model. The spectral criterion concerns first-order response, not arbitrary finite loss. Numerical advantages are restricted to the same one-quantum resonance operating branch, rather than unrestricted coherent control; the proposed reservoir realization is simulated, not experimentally demonstrated.