Tony Dorlas

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{sub 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 by Christandl et al., Phys. Rev. Lett. 92, 187902 (2004)

The coding theorem for a class of quantum channels with long-term memory

In this paper, we consider the transmission of classical information through a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. Hence, the memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. We prove the coding theorem and weak converse for this class of channels. The main techniques that we employ are a quantum version of Feinsteins fundamental lemma (Feinstein A 1954 IRE Trans. PGIT 4 2–22, Khinchin A I 1957 Mathematical Foundations of Information Theory: II. On the Fundamental Theorems of Information Theory (New York: Dover) chapter IV) and a generalization of Helstroms theorem (Helstrom C W 1976 Quantum detection and estimation theory Mathematics in Science and Engineering vol 123 (London: Academic)).

Properties of subentropy

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevos theorem. Here we establish a series of properties of subentropy, paralleling the well-developed analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for min-entropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classical-quantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally, we give an operational interpretation of subentropy within classical information theory.

ASYMPTOTIC FEYNMAN-KAC FORMULAE FOR LARGE SYMMETRISED SYSTEMS OF RANDOM WALKS

We study large deviations principles for N random processes on the lattice Z d with finite time horizon (0 ,β ) under a symmetrised measure where all initial and terminal points are uniformly given by a random permutation. That is, given a permu- tation σ of N elements and a vector (x1 ,...,x N )o fN initial points we let the random processes terminate in the points (xσ(1) ,...,x σ(N )) and then sum over all possible per- mutations and initial points, weighted with an initial distribution. There is a two-level random mechanism and we prove two-level large deviations principles for the mean of empirical path measures, for the mean of paths and for the mean of occupation local times under this symmetrised measure. The symmetrised measure cannot be written as any product of single random process distributions. We show a couple of important applications of these results in quantum statistical mechanics using the Feynman-Kac formulae representing traces of certain trace class operators. In particular we prove a non-commutative Varadhan Lemma for quantum spin systems with Bose-Einstein statistics and mean field interactions. A special case of our large deviations principle for the mean of occupation local times of N simple random walks has the Donsker-Varadhan rate function as the rate function for the limit N →∞ but for finite time β. We give an interpretation in quantum statistical mechanics for this surprising result.

Classical capacity of quantum channels with memory

We investigate the classical capacity of two quantum channels with memory: a periodic channel with depolarizing channel branches and a convex combination of depolarizing channels. We prove that the capacity is additive in both cases. As a result, the channel capacity is achieved without the use of entangled input states. In the case of a convex combination of depolarizing channels the proof provided can be extended to other quantum channels whose classical capacity has been proven to be additive in the memoryless case.

C*-algebraic approach to the Bose-Hubbard model

We give a new derivation of the variational formula for the pressure of the long-range-hopping Bose-Hubbard model, which was first proven by Bru and Dorlas [J. Stat. Phys. 113, 177 (2003)]. The proof is analogous to that of a theorem on noncommutative large deviations introduced by Petz et al. [Commun. Math. Phys. 121, 271 (1989)] and could similarly be extended to more general Bose systems of mean-field type. We apply this formalism to prove Bose-Einstein condensation for the case of small coupling.

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. This class of channels was introduced by Datta and Dorlas in (J. Phys. A, Math. Theor. 40:8147–8164, 2007), where its product state capacity was evaluated.

Large deviation approach to the generalized random energy model

The generalized random energy model is a generalization of the random energy model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the Sherrington–Kirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A complete solution for the thermodynamics in the general case was given by Capocaccia et al. Here we use large deviation theory to analyse the model in a very straightforward way. We also show that the variational expression for the free energy can be evaluated easily using the Cauchy–Schwarz inequality.

A quantum version of Feinstein's Theorem and its application to channel coding

In this paper, a quantum version of Feinsteins theorem is developed. This is then used to give a completely self-contained proof of the direct channel coding theorem, for transmission of classical information through a quantum channel with Markovian correlated noise. Our proof does not rely on the Holevo-Schumacher-Westmoreland (HSW) theorem. In addition, for the case of memoryless channels, our method yields an alternative proof of the HSW Theorem

CALCULATING A MAXIMIZER FOR QUANTUM MUTUAL INFORMATION

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.