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We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open systems dynamics, are related to each other by the Holevo quantity. This, in turn, can be further split into an information gain rate and loss rate, which provide conditions for the existence of informational steady-states (ISSs), i.e. stationary states of a conditional dynamics that are maintained owing to the unbroken acquisition of information. We illustrate the applicability of our framework through several examples.
We discuss the problem of estimating a frequency via N-qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional sta
Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing
We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit, the conditional
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring. Optimal pat
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be bu