2,862 research outputs found
Stochastic Matrix Product States
The concept of stochastic matrix product states is introduced and a natural
form for the states is derived. This allows to define the analogue of Schmidt
coefficients for steady states of non-equilibrium stochastic processes. We
discuss a new measure for correlations which is analogous to the entanglement
entropy, the entropy cost , and show that this measure quantifies the bond
dimension needed to represent a steady state as a matrix product state. We
illustrate these concepts on the hand of the asymmetric exclusion process
Dissipation and lag in irreversible processes
When a system is perturbed by the variation of external parameters, a lag
generally develops between the actual state of the system and the equilibrium
state corresponding to the current parameter values. We establish a
microscopic, quantitative relation between this lag and the dissipated work
that accompanies the process. We illustrate this relation using a model system.Comment: 6 pages, 3 figures, accepted for publication in EP
Optimal evaluation of single-molecule force spectroscopy experiments
The forced rupture of single chemical bonds under external load is addressed.
A general framework is put forward to optimally utilize the experimentally
observed rupture force data for estimating the parameters of a theoretical
model. As an application we explore to what extent a distinction between
several recently proposed models is feasible on the basis of realistic
experimental data sets.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.
Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data
We introduce a procedure to infer the interactions among a set of binary
variables, based on their sampled frequencies and pairwise correlations. The
algorithm builds the clusters of variables contributing most to the entropy of
the inferred Ising model, and rejects the small contributions due to the
sampling noise. Our procedure successfully recovers benchmark Ising models even
at criticality and in the low temperature phase, and is applied to
neurobiological data.Comment: Accepted for publication in Physical Review Letters (2011
Lower bound on the number of Toffoli gates in a classical reversible circuit through quantum information concepts
The question of finding a lower bound on the number of Toffoli gates in a
classical reversible circuit is addressed. A method based on quantum
information concepts is proposed. The method involves solely concepts from
quantum information - there is no need for an actual physical quantum computer.
The method is illustrated on the example of classical Shannon data compression.Comment: 4 pages, 2 figures; revised versio
Kinetics and thermodynamics of first-order Markov chain copolymerization
We report a theoretical study of stochastic processes modeling the growth of
first-order Markov copolymers, as well as the reversed reaction of
depolymerization. These processes are ruled by kinetic equations describing
both the attachment and detachment of monomers. Exact solutions are obtained
for these kinetic equations in the steady regimes of multicomponent
copolymerization and depolymerization. Thermodynamic equilibrium is identified
as the state at which the growth velocity is vanishing on average and where
detailed balance is satisfied. Away from equilibrium, the analytical expression
of the thermodynamic entropy production is deduced in terms of the Shannon
disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is
recovered in the fully irreversible growth regime. The theory also applies to
Bernoullian chains in the case where the attachment and detachment rates only
depend on the reacting monomer
Entanglement combing
We show that all multi-partite pure states can, under local operations, be
transformed into bi-partite pairwise entangled states in a "lossless fashion":
An arbitrary distinguished party will keep pairwise entanglement with all other
parties after the asymptotic protocol - decorrelating all other parties from
each other - in a way that the degree of entanglement of this party with
respect to the rest will remain entirely unchanged. The set of possible
entanglement distributions of bi-partite pairs is also classified. Finally, we
point out several applications of this protocol as a useful primitive in
quantum information theory.Comment: 5 pages, 1 figure, replaced with final versio
Natural Metric for Quantum Information Theory
We study in detail a very natural metric for quantum states. This new
proposal has two basic ingredients: entropy and purification. The metric for
two mixed states is defined as the square root of the entropy of the average of
representative purifications of those states. Some basic properties are
analyzed and its relation with other distances is investigated. As an
illustrative application, the proposed metric is evaluated for 1-qubit mixed
states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto
Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation
We present a continuous-variable quantum key distribution protocol combining
a discrete modulation and reverse reconciliation. This protocol is proven
unconditionally secure and allows the distribution of secret keys over long
distances, thanks to a reverse reconciliation scheme efficient at very low
signal-to-noise ratio.Comment: 4 pages, 2 figure
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