Related papers: Double Markovity for quantum systems
In this paper we propose a continuous-time, dissipative Markov dynamics that asymptotically drives a network of n-dimensional quantum systems to the set of states that are invariant under the action of the subsystem permutation group. The…
We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-Weyl duality between a two-parameter quantum group and a…
Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
A central problem in quantum information is determining quantum-classical boundaries. A useful notion of classicality is provided by the quasiprobability formulation of quantum theory. In this framework, a state is called classical if it is…
Consider estimating the G-formula for the counterfactual mean outcome under a given treatment regime in a longitudinal study. Bang and Robins provided an estimator for this quantity that relies on a sequential regression formulation of this…
Kirkwood-Dirac (KD) quasiprobability is a quantum analog of classical phase space probability. It offers an informationally complete representation of quantum state wherein the quantumness associated with quantum noncommutativity manifests…
Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds.…
It is a well-established fact in quantum information theory, that uniform averaging over the collective action of a unitary group on a multipartite quantum state projects the state to a form equivalent to a permutation operator of the…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
After the mathematical notion of "Micro-Macro Duality" for understanding mutual relations between microsopic quantum systems (Micro) and their macroscopic manifestations (Macro) is explained on the basis of the notion of sectors and order…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance (NMR) setup and employing geometric discord, we evaluate the quantum correlations of a…
A Markovian open quantum system which relaxes to a unique steady state $\rho_{ss}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by Karasik and Wiseman [Phys. Rev.…
In 2018, Renes [IEEE Trans. Inf. Theory, vol. 64, no. 1, pp. 577-592 (2018)] (arXiv:1701.05583) developed a general theory of channel duality for classical-input quantum-output (CQ) channels. That result showed that a number of well-known…
A concise and self-contained derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Many previously known results are re-derived, revised, some of them completed or corrected. Using as simple method…
We present an iterative algorithm based on semidefinite programming (SDP) for computing the quantum smooth max-mutual information $I^\varepsilon_{\max}(\rho_{AB})$ of bipartite quantum states in any dimension. The algorithm is accurate if a…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state space of the system; the quantum state…
The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right…
We exploit quantum discord to detect quantum correlations for two-state Markov binary, which has broad of applications in quantum information theory. To calculate the correlation in Markov-binary, We wrote a transition matrix elements based…