13 research outputs found
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.Comment: 31 pages, 2 figures. 2nd revision. Misprints corrected and 1 figure
adde
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 given by convex
combinations of product channels. Hence, the memory of such channels is 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 Feinstein's Fundamental Lemma and a
generalization of Helstrom's Theorem.Comment: Some typos correcte
Random Walks on a Complete Graph: A Model for Infection
We introduce a new model for the infection of one or more subjects by a single agent and calculate the probability of infection after a fixed length of time. We model the agent and subjects as random walkers on a complete graph of N sites, jumping with equal rates from site to site. When one of the walkers is at the same site as the agent for a length of time τ, we assume that the infection probability is given by an exponential law with parameter γ, i.e. q(τ) = 1 − e^(−γτ). We introduce the boundary condition that all walkers return to their initial site (‘home’) at the end of a fixed period T. We also assume that the incubation period is longer than T so that there is no immediate propagation of the infection. In this model, we find that for short periods T, i.e. γT << 1 and T << 1, the infection probability is remarkably small and behaves like T^3. On the other hand, for large T, the probability tends to 1 (as might be expected) exponentially. However, the dominant exponential rate is given approximately by 2γ/((2+γ)N) and is therefore small for large N
The invalidity of a strong capacity for a quantum channel with memory
The strong capacity of a particular channel can be interpreted as a sharp
limit on the amount of information which can be transmitted reliably over that
channel. To evaluate the strong capacity of a particular channel one must prove
both the direct part of the channel coding theorem and the strong converse for
the channel. Here we consider the strong converse theorem for the periodic
quantum channel and show some rather surprising results. We first show that the
strong converse does not hold in general for this channel and therefore the
channel does not have a strong capacity. Instead, we find that there is a scale
of capacities corresponding to error probabilities between integer multiples of
the inverse of the periodicity of the channel. A similar scale also exists for
the random channel.Comment: 7 pages, double column. Comments welcome. Repeated equation removed
and one reference adde
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 -qubit spin networks
of identical qubit couplings, we show that 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.Comment: 12 pages, 3 figures with updated reference
Classical capacity of quantum channels with general Markovian correlated noise
The classical capacity of a quantum channel with arbitrary Markovian
correlated noise is evaluated. For the general case of a channel with long-term
memory, which corresponds to a Markov chain which does not converge to
equilibrium, the capacity is expressed in terms of the communicating classes of
the Markov chain. For an irreducible and aperiodic Markov chain, the channel is
forgetful, and one retrieves the known expression for the capacity