Related papers: Necessary criterion for approximate recoverability
Transforming a causal system from a given initial state to a desired target state is an important task permeating multiple fields including control theory, biology, and materials science. In causal models, such transformations can be…
This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive…
A class of examples is constructed to show that for strictly stationary Markov chains that are reversible, the simultaneous mixing rates for the $\rho$-mixing and strong mixing ($\alpha$-mixing) conditions can be fairly arbitrary, within…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
Consider additive functionals of a Markov chain $W_k$, with stationary (marginal) distribution and transition function denoted by $\pi$ and $Q$, say $S_n=g(W_1)+...+g(W_n)$, where $g$ is square integrable and has mean 0 with respect to…
When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This letter shows that entanglement lost in the manipulation can be…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…
The results from the ATLAS and CMS experiment at the Large Hadron Collider indicate the existence of a top-quark pair bound state near the $\ttbar$ threshold region. We present a method relying on Recursive Jigsaw Reconstruction to…
Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite…
Using an exactly solvable model of the Wigner-Weisskopf atom it is shown that an unstable quantum state cannot be recovered completely by the procedure involving detection of the decay products followed by creation of the time reversed…
When the state space of a discrete state space positive recurrent Markov chain is infinite or very large, it becomes necessary to truncate the state space in order to facilitate numerical computation of the stationary distribution. This…
We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment.…
The separability of bipartite non-Gaussian states is studied by applying the realignment criterion with the technique of functional analysis. The realignment criterion is given as one inequality in contrast to the infinitive number of…
Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as…
We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…