4,167 research outputs found
Noise-Free Measurement of Harmonic Oscillators with Instantaneous Interactions
We present a method of measuring the quantum state of a harmonic oscillator
through instantaneous probe-system selective interactions of the
Jaynes-Cummings type. We prove that this scheme is robust to general
decoherence mechanisms, allowing the possibility of measuring fast-decaying
systems in the weak-coupling regime. This method could be applied to different
setups: motional states of trapped ions, microwave fields in cavity/circuit
QED, and even intra-cavity optical fields.Comment: 4 pages, no figure, published in Physical Review Letter
Entropy Production of Doubly Stochastic Quantum Channels
We study the entropy increase of quantum systems evolving under primitive,
doubly stochastic Markovian noise and thus converging to the maximally mixed
state. This entropy increase can be quantified by a logarithmic-Sobolev
constant of the Liouvillian generating the noise. We prove a universal lower
bound on this constant that stays invariant under taking tensor-powers. Our
methods involve a new comparison method to relate logarithmic-Sobolev constants
of different Liouvillians and a technique to compute logarithmic-Sobolev
inequalities of Liouvillians with eigenvectors forming a projective
representation of a finite abelian group. Our bounds improve upon similar
results established before and as an application we prove an upper bound on
continuous-time quantum capacities. In the last part of this work we study
entropy production estimates of discrete-time doubly-stochastic quantum
channels by extending the framework of discrete-time logarithmic-Sobolev
inequalities to the quantum case.Comment: 24 page
Relative Entropy Convergence for Depolarizing Channels
We study the convergence of states under continuous-time depolarizing
channels with full rank fixed points in terms of the relative entropy. The
optimal exponent of an upper bound on the relative entropy in this case is
given by the log-Sobolev-1 constant. Our main result is the computation of this
constant. As an application we use the log-Sobolev-1 constant of the
depolarizing channels to improve the concavity inequality of the von-Neumann
entropy. This result is compared to similar bounds obtained recently by Kim et
al. and we show a version of Pinsker's inequality, which is optimal and tight
if we fix the second argument of the relative entropy. Finally, we consider the
log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel
and use a quantum version of Shearer's inequality to prove a uniform lower
bound.Comment: 21 pages, 3 figure
Corrigendum and addendum to “non-autonomous quasilinear elliptic equations and Ważewski’s principle”
In this addendum we fill a gap in a proof and we correct some results appearing in [12]. In the original paper [12] we classified positive solutions for the following equation ∆pu + K(r)uσ−1 = 0 where r = |x|, x ∈ ℝn, n > p > 1, σ = np/(n − p) and K(r) is a function strictly positive and bounded. In fact [12] had two main purposes. First, to establish asymptotic conditions which are sufficient for the existence of ground states with fast decay and to classify regular and singular solutions: these results are correct but need some non-trivial further explanations. Second to establish some computable conditions on K which are sufficient to obtain multiplicity of ground states with fast decay in a non-perturbation context. Also in this case the original argument contained a flaw: here we correct the assumptions of [12] by performing a new nontrivial construction. A third purpose of this addendum is to generalize results of [12] to a slightly more general equation ∆pu + rδK(r)uσ(δ)−1 = 0 where δ > −p, and σ(δ) = p(n + δ)/(n − p)
Anyons and transmutation of statistics via vacuum induced Berry phase
We show that bosonic fields may present anyonic behavior when interacting
with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished
via the interaction of a two-level system with two quantized modes of a
harmonic oscillator; under suitable conditions, the system acquires a
fractional geometric phase. A crucial role is played by the entanglement of the
system eigenstates, which provides a two-dimensional confinement in the
effective evolution of the system, leading to the anyonic behavior. For a
particular choice of parameters, we show that it is possible to transmute the
statistics of the system continually from fermions to bosons. We also present
an experimental proposal, in an ion-trap setup, in which fractional statistical
features can be generated, controlled, and measured
Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
As photons do not interact with each other, it is interesting to ask whether
photonic systems can be modified to exhibit the phases characteristic of
strongly coupled many-body systems. We demonstrate how a Mott insulator type of
phase of excitations can arise in an array of coupled electromagnetic cavities,
each of which is coupled resonantly to a {\em single} two level system
(atom/quantum dot/Cooper pair) and can be individually addressed from outside.
In the Mott phase each atom-cavity system has the same integral number of net
polaritonic (atomic plus photonic) excitations with photon blockade providing
the required repulsion between the excitations in each site. Detuning the
atomic and photonic frequencies suppresses this effect and induces a transition
to a photonic superfluid. We also show that for zero detuning, the system can
simulate the dynamics of many body spin systems.Comment: 4 pages, 3 figure
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