相关论文: Robustness of quantum Markov chains

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>…

Starting from a Markov chain with a finite alphabet, we consider the chain obtained when all but one symbol are undistinguishable for the practitioner. We study necessary and sufficient conditions for this chain to have continuous…

In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…

How much information can a transmitted physical system fundamentally communicate? We introduce the principle of quantum information causality, which states the maximum amount of quantum information that a quantum system can communicate as a…

Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…

Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a "quantum information" to quantum mechanical degree of freedom equal to Hausdorff area of the deviation from a…

Given a quantum channel and a state which satisfy a fixed point equation approximately (say, up to an error $\varepsilon$), can one find a new channel and a state, which are respectively close to the original ones, such that they satisfy an…

We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the…

We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the…

The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…

Consider an open quantum system with (discrete-time) Markovian dynamics. Our task is to store information in the system in such a way that it can be retrieved perfectly, even after the system is left to evolve for an arbitrarily long time.…

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$…

The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the…

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…

Quantum mechanics offers the possibility of unconditionally secure communication between multiple remote parties. Security proofs for such protocols typically rely on bounding the capacity of the quantum channel in use. In a similar manner,…

Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is…

We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…

The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…