Related papers: Theory of Ergodic Quantum Processes
In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…
Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless…
Quantum entanglement manifests as a distinctive correlation between particles that transcends classical boundaries when their quantum states cannot be described independently. On the other hand, as quantum systems interact with their…
Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for…
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be…
Motivated by stability questions on piecewise deterministic Markov models of bacterial chemotaxis, we study the long time behavior of a variant of the classic telegraph process having a non-constant jump rate that induces a drift towards…
The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels.…
We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced sophisticated…
Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the…
In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general…
We study the asymptotic bipartite entanglement entropy of the quantum trajectories of a free-fermionic system, when subject to a continuous nonlocal monitoring. The measurements are described by Gaussian-preserving two-point operators,…
The open-system dynamics of entanglement plays an important role in the assessment of the robustness of quantum information processes and also in the investigation of the classical limit of quantum mechanics. Here we show that, subjacent to…
Ergodic quantum many-body systems undergoing unitary dynamics evolve towards increasingly entangled states characterized by an extensive scaling of entanglement entropy with system volume. At the other extreme, quantum systems repeatedly…
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…
Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network…
The presence of quantum multipartite entanglement implies the existence of a thermodynamic quantity known as the ergotropic gap, which is defined as the difference between the maximal global and local extractable works from the system. We…