arXiv subjects

Tony C. Dorlas

Publications and source records attributed to Tony C. Dorlas.

7 recordsLinked to original sources

arXiv2025

On the Wasserstein distance and the Dobrushin uniqueness theorem

In this paper, we revisit the Dobrushin uniqueness theorem for Gibbs measures of lattice systems of interacting particles at thermal equilibrium. In a nutshell, Dobrushin's uniqueness theorem provides a practical way to derive sufficient conditions on the inverse temperature and/or model parameters assuring uniqueness of Gibbs measures by reducing the uniqueness problem to a suitable estimate of the Wasserstein distance between pairs of 1-point Gibbs measures with different boundary conditions. After proving a general result of completeness for the Wasserstein distance, we reformulate the Dobrushin uniqueness theorem in a convenient form for lattice systems of interacting particles described by Hamiltonians that are not necessarily translation-invariant with possibly infinite-range pair-potentials and with general complete metric spaces as single-spin spaces. Our reformulation includes existence, and covers both classical lattice systems and the Euclidean version of quantum lattice systems. Further, a generalization to the Dobrushin-Shlosman theorem for translation-invariant lattice systems is given. Subsequently, we give a series of applications of these uniqueness criteria to some high-temperature classical lattice systems including the Heisenberg, Potts and Ising models. An application to classical lattice systems for which the local Gibbs measures are convex perturbations of Gaussian measures is also given.

math-ph↗

arXiv2020

A combinatorial identity with applications to forest graphs

We give an elementary proof of an interesting combinatorial identity which is of particular interest in graph theory and its applications. Two applications to enumeration of forests with closed-form expressions are given.

math.CO↗

arXiv2019

Correlation of clusters: Partially truncated correlation functions and their decay

In this article, we investigate partially truncated correlation functions (PTCF) of infinite continuous systems of classical point particles with pair interaction. We derive Kirkwood-Salsburg-type equations for the PTCF and write the solutions of these equations as a sum of contributions labelled by certain forests graphs, the connected components of which are tree graphs. We generalize the method introduced by R.A. Minlos and S.K. Poghosyan (1977) in the case of truncated correlations. These solutions make it possible to derive strong cluster properties for PTCF which were obtained earlier for lattice spin systems.

math-ph↗

arXiv2019

Simulating quantum circuits by adiabatic computation: improved spectral gap bounds

Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a mapping of a quantum circuit to an an adiabatic evolution, and then showing that the minimum spectral gap of the adiabatic Hamiltonian is at least inverse polynomial in the number of computational steps $L$. In this paper we provide two simplified proofs that the gap is inverse polynomial. Both proofs result in the same lower bound for the minimum gap, which for $L \gg 1$ is $\min_sΔ\gtrsim π^2 / [8(L+1)^2]$, an improvement over previous estimates. Our first method is a direct approach based on an eigenstate ansatz, while the the second uses Weyl's theorem to leverage known exact results into a bound for the gap. Our results suggest that it may be possible to use these methods to find bounds for spectral gaps of Hamiltonians in other scenarios.

quant-ph↗

arXiv2010

Entanglement of a two-particle Gaussian state interacting with a heat bath

The effect of a thermal reservoir is investigated on a bipartite Gaussian state. We derive a pre-Lindblad master equation in the non-rotating wave approximation for the system. We then solve the master equation for a bipartite harmonic oscillator Hamiltonian with entangled initial state. We show that for strong damping the loss of entanglement is the same as for freely evolving particles. However, if the damping is small, the entanglement is shown to oscillate and eventually tend to a constant nonzero value.

quant-ph↗

arXiv2009

Entanglement Assisted Classical Capacity of a Class of Quantum Channels with Long-Term Memory

In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible.

quant-ph↗

arXiv2004

Perfect Transfer of Arbitrary States in Quantum Spin Networks

We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2\log_3 N$ is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done in PRL 92, 187902.

quant-ph↗