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Current reconfiguration techniques are based on starting the system in a consistent configuration, in which all participating entities are in their initial state. Starting from that state, the system must preserve consistency as long as a…
The joint state of a continuously monitored quantum system and the classical filtered measurement record has recently been shown to be described by a quantum Fokker-Planck master equation [Phys. Rev. Lett. 129, 050401 (2022)]. We present a…
In this work, we introduce a new space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable, and a modified Hilbert transformation is used. For this…
This work studies remote state estimation of multiple linear time-invariant systems over shared wireless time-varying communication channels. We model the channel states by a semi-Markov process which captures both the random holding period…
In this paper we determine quantitative stability bounds for the Hessian of entropic potentials, \ie, the dual solution to the entropic optimal transport problem. To the authors' knowledge this is the first work addressing this second-order…
This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…
The problem of stability of the optimal filter is revisited. The optimal filter (or filtering process) is the conditional probability of the current state of some stochastic process (the signal process), given both present and past values…
The theory of continuous quantum measurement allows to reconstruct the state $\rho_t$ of a system from a continuous stochastic measurement record $I_t$. However, this truly continuous-time signal $I_t$ is never available in practice. In…
In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
State-of-the-art noisy intermediate-scale quantum computers require low-complexity techniques for the mitigation of computational errors inflicted by quantum decoherence. Symmetry verification constitutes a class of quantum error mitigation…
This work studies a stabilization technique for first-order hyperbolic differential equations used in DNA transcription modeling. Specifically we use the Lighthill-Whitham-Richards Model with a nonlinear Greenshield's velocity proposed in…
In this paper we establish the meta-stability of travelling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in…
Here, we are concerned with comparing estimation schemes for the quantum state under continuous measurement (quantum trajectories), namely quantum state filtering and, as introduced by us [Phys. Rev. Lett. 115, 180407 (2015)], quantum state…
We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $\lambda$ is varied across a quantum phase transition. For this purpose we…
Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation…