相关论文: Unification of stochastic matrices and quantum ope…

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…

The theory of quantum states over time extends the density operator formalism into the temporal domain, providing a unified of treatment of timelike and spacelike separated systems in quantum theory. Although recent results have…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…

Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…

The evolution of a quantum system, appropriate to describe nano-magnets, can be mapped on a Markov process, continuous in $\beta$. The mapping implies a probability assignment that can be used to study the probability density (PDF) of the…

The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure…

As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase…

We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple…

In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$, $\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is the initial state, the the state of the system is either oscillatory or convergent to a…

We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…

We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…

We establish a direct connection of quantum Markovianity of an open quantum system to its classical counterpart by generalizing the criterion based on the information flow. Here, the flow is characterized by the time evolution of Helstrom…

Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes…

It is shown that large deviation statistical quantities of the discrete time, finite state Markov process $P_{n+1}^{(j)}=\sum_{k=1}^NH_{jk}P_n^{(k)}$, where P_n^{(j)} is the probability for the j-state at the time step n and H_{jk} is the…

A semi-Markov process method for obtaining general counting statistics for open quantum systems is extended to the scenario of resetting. The simultaneous presence of random resets and wave function collapses means that the quantum jump…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…

It has been found that Markovian quantum dissipative processes, described by the Lindblad equation, may have attractive steady-state manifolds, in which dissipation and decoherence can play a positive role to quantum information processing.…

Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…

We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…