Paolo Aniello (Napoli)
Group-theoretical methods for quantum
mechanics on phase space and star products
The phase space formulation of
quantum mechanics and the concept of star product of functions are remarkable
achievements of theoretical physics. The prototypes of these notions are the
formalism of Wigner distributions (which is strictly related to the Weyl
system) and the Groenewold-Moyal star product. Adopting a group-theoretical
point of view, we consider phase space realizations of quantum mechanics and
star products that are associated with representations of locally compact
groups. The main properties of this general approach and the connection with
the standard Weyl-Wigner–Groenewold-Moyal formalism are discussed.
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Manuel Asorey (Saragoza)
Quantum Boundary Effects
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F. Benatti (Trieste)
3 Lectures on Entropy in Quantum Information
1. Von
Neumann entropy and entanglement
2.
Quantum relative entropy and entanglement of formation
3. Quantum entropy and quantum compression
theorems
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Benenti
Giuliano (Como-Insubria)
How complex is quantum motion?
In
classical mechanics the complexity of a dynamical system is characterized by
the rate of local exponential instability which effaces the memory of initial
conditions and leads to practical irreversibility. In striking contrast,
quantum mechanics appears to exhibit strong memory of the initial state. Here
we introduce a notion of complexity for a quantum system and relate it to its
stability and reversibility properties.
References:
[1] G.
Benenti and G. Casati, "How complex is quantum motion?", preprint
arXiv:0808.3243
[quant-ph],
Phys. Rev. E (in press).
[2]
V.V. Sokolov, O.V. Zhirov, G. Benenti and G. Casati, "Complexity of
quantum states and
reversibility of quantum motion", Phys. Rev. E 78, 046212
(2008).
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Fabio Chiarello (Roma I)
Ultrafast manipulation of a superconducting qubit
with flux pulses
The
state of a superconducting double SQUID qubit can be completely and
effectively manipulated by using simple digital pulses applied on the
magnetic fluxes controlling the device, in contrast with the typical
manipulation based on microwave pulses. We observed coherent oscillations at
different temperatures, in good agreement with the theoretical predictions,
and characterized by a very high
frequency (up to 20GHz), in contrast with the slower
microwave manipulation (with oscillation frequencies below 1GHz). This allows
an high number of visible oscillations (about 200)
within the coherence time (about 10ns), one of the best results among the
present superconducting qubits. We discuss the obtained results and the
relative problems.
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Dariusz Chruscinski (Torun)
Spectral properties of entanglement witnesses
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A. De Pasquale (Bari)
Phase
transitions of entanglement
We
introduce a statistical approach to the study of bipartite entanglement for
large quantum systems; in particular our approach is based on a random matrix
model that describes the purity of a party. We write the expression of a
partition function, with a fictitious temperature and determine the spectrum
of the reduced density matrix that maximize it. In
the case of pure states the presence of a phase transition has been unveiled.
Here we generalize and discuss this approach to the case of mixed states.
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Antonio D'Arrigo
Enhancement of transmission rates in quantum memory
channels with damping
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A.
Florio (INRIM Torino-Bari)
Optimal estimation of entanglement
Entanglement
is perhaps the most distinctive feature of quantum mechanics and the most
relevant resource for quantum information processing. One of the most
important problem connected to entanglement is that
it does not correspond to an observable and than its evaluation always
corresponds to an estimation procedure, where the amount of entanglement is
inferred from the measurements of one or more proper observables. Our aim is
to evaluate experimentally the ultimate bound to precision posed by quantum
mechanics, i.e. the smallest value of the
entanglement that can be discriminated, and to determine the
optimal measurements achieving those bounds. For this purpose we will compare
theoretical prediction with various entanglement measures applied to several
non-maximally and mixed photon entangled states produced via PDC.
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Giuseppe Florio (Bari)
Entanglement of two blocks of spins in the critical
Ising model
We
compute the entropy of entanglement of two blocks of L spins at a distance d
in the ground state of an Ising chain in an external transverse magnetic
field. We numerically study the von Neumann entropy for different values of
the transverse field. At the critical point we obtain analytical results for
blocks of size L=1 and 2. In
the general case, the critical entropy is shown to be additive when d goes to
infinity. Finally, based on simple arguments, we derive an expression for the
entropy at the
critical point as a function of both L and d. This formula
is in excellent agreement with numerical results.
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Vittorio Giovannetti (SNS Pisa)
Capacities of lossy bosonic memory channels
We
introduce a general model for a lossy bosonic memory channel and calculate
the classical and the quantum capacity, proving that coherent state encoding
is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold
concatenation of the memory channel is unitarily equivalent to the direct
product of n single-mode lossy bosonic channels.
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Andrzej Kossakowski (Torun)
On the structure of generarors of non-Markovian
Master Equations
The
structure of generators of non-markovian master equations which preserve
complete positivity is presented.
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M. Ligabo (Bari)
Radon vs Symplectic: the M^2 transform
We
compare the Radon and the symplectic transform in a few simple but
interesting examples.
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Cosmo Lupo (Camerino)
Information capacity of quantum channels with memory
The
biggest limitation in the efficiency of quantum information processing is the
unavoidable presence of noise, which causes a distortion of quantum
information. In the case of communication through noisy quantum channel,
error-correcting codes are used to overcome this problem. The messages are
encoded into codewords, which are in turn sent through the channel. The
communication is hence said to be reliable if the probability of error, at
the decoding stage at the output of the channel, vanishes in the limit of
infinite number of channel uses. The aim in communication theory is to
optimize the rate of the reliable communication, i.e. the ratio of the size
of the message to the corresponding codeword. The optimal rate of reliable
information transmission is by definition the capacity of the channel. Several
notions of capacities for quantum channels have been defined, depending on
whether quantum or classical information is trasmitted, and if additional
resorces, such as quantum entanglement between the communicating parties, are
available. The simplest model for a quantum channel is a memoryless one,
where the noise acts independently at each use of the channel. The memoryless
case can be viewed as an approximation for a more general and realistic model
of quantum channel, where correlations exist among the noise acting at
different channel uses and the action of the channel at each use depends on
the previous ones. As an application, I introduce and discuss a general model
for a memory channel acting on bosonic system.
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M. A. Man'ko (Lebedev, Moscow)
Renyi, Shannon, and
Tsallis Entropies of Quantum States and New Entropic Uncertainty Relations
The
known entropies of quantum states (von Neumann entropy, Wehrl entropy) and
entropies associated with the probabilities describing quantum states in the
probability representation of quantum mechanics like Shannon
entropy, Renyi entropy, and Tsallis entropy are discussed.
Subadditivity
and strong subadditivity for
Shannon
entropy
of composed quantum sistems as well as entropic uncertainty relations are
presented.
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Volodya Manko (Lebedev, Moscow)
Quantum tomography and its possible applications
Tomographic
approach to quantum states desription where the states are associated with
fair probability distribution functions is reviewed. Different kinds of the
tomographic probability distributions for states with continuous variables
-position,momentum,photon quadrature components,like symplectic
tomography,Fresnel tomography,optical tomography and photon number tomography
are discussed as well as different kinds of discrete variables systems like
spin systems ,qubits,qudits are considered from tomographic probability
desription point of view.
Some
applications like detection of entanglement by qubit portrait method of qudit
states and two-mode photon states are presented.
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Luigi Martina (Lecce)
Entanglement of coupled oscillators and Hartree-Fock
Approximation
Approximation Our
goal is to clarify the relation between entanglement and correlation energy
in a bipartite system with infinite dimensional Hilbert space. To this aim we
consider the completely solvable Moshinsky's model of two linearly coupled harmonic
oscillators. Also for small values of the couplings the entanglement of the
ground state is nonlinearly related to the correlation energy, involving
logarithmic or algebraic corrections. Then, looking for witness observables
of the entanglement, we show how to give a physical interpretation of the
correlation energy. In particular,
we have proven that there exists a set of separable states, continuously
connected with the Hartree-Fock state, which may have a larger overlap with
the exact ground state, but also a larger energy expectation value. In this
sense, the correlation energy provides an entanglement gap, i.e. an energy
scale, under which measurements performed on the 1-particle harmonic
sub-system can
discriminate the ground state from any other separated state of
the system. However, in order to verify the generality of the procedure, we
have compared the energy distribution cumulants for the 1-particle harmonic
sub-system of the Moshinsky's model with the case of a coupling with a
damping Ohmic bath at 0 temperature.
***********************
Alice Meda (INRIM Torino)
Sub Shot Noise Spatial Correlation Measurement
without background subtraction
The
possibility of imaging a weak object with a level of noise below the minimum
threshold (Shot Noise) imposed by classical light detection is one of the
most interesting results of the developing field christened Quantum Imaging
[1]. A little more in detail, this scheme is based on exploiting spatial
quantum correlations of biphotons emitted by parametric down conversion
(PDC): indeed, the correlated noise pattern measured on one branch of PDC can
be subtracted from the image of an object placed in the other branch. The
image of the object, if hidden in the noise, can be in principle restored. Experimentally,
to reach this high sensitivity imaging, a high photon flux with negligible
background noise regime is required; this means that an under shot noise
measurement must be reached without background subtraction [2], a result
that, up to now, was not achieved. We report this achievement, i.e. a clear
observation of sub shot noise spatial regime without background subtraction,
detailing the description of the experimental setup and of the main results.
[1] M. I.
Kolobov editor Quantum Imaging, Springer Verlag, Singapore, (2007)
[2] E.
Brambilla et al, gHigh -sensitivity imaging with multi-mode twin beamsh,
Phys. Rev. A
77, 053807/1-11(2008)
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Eliano Pessa (Pavia)
QUANTUM
SIGNATURE IN BRAIN SIGNALS
In
recent times the question of the quantum nature of brain has become a very
important issue, not only for the thinking processes themselves, but also for
the relationship with quantum computers.
Such a
question can be delt with only by resorting to an integration of theoretical
constructs with techniques of data analysis. In this contribution some
proposals in this domain are discussed and compared with previous findings
already present in the literature.
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Francesco Plastina (Calabria)
Global vs local control of entanglement in a spin
chain
We
consider an XX S=1/2 spin chain in transverse field, discussing the finite
size properties of such model, which shows a ground state instability with a
sequence of sudden entanglement jumps when the (global) magnetic field is
varied within the critical region. We also consider the effect of local
magnetic impurities. In the disordered phase, such defects give rise to an
Anderson-like localization of entanglement, that can
be exploited for quantum information storage. Furthermore, the ability to
locally control the field allows one to manipulate the entanglement dynamics
of entanglement its transfer along the chain. In the quasi-long range ordered
phase, local impurities produce an entanglement reshuffling along the chain,
with local enhancements or suppressions that depend on the distance from the
impurity.
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A.
Porzio/ S. Fornaro (Napoli)
Homodyning continuous variables bipartite entangled
states: a review on recent experimental results and data analysis strategies
for a reliable state reconstruction.
By
means of the type-II below threshold optical parametric oscillator (OPO),
Gaussian bipartite entangled states are generated. In this contribution after
a review on the entire covariance matrix (CM) reconstruction obtained by
using a single homodyne detector we will focus on possible strategies for
improving the reliability of the statistical analysis of homodyne data. In
particular we will focus on the proof of Gaussianity and on the possibility
of removing any correlation nested in
the data. A review on the different criteria for bipartite Gaussian state
applied to real data is given.
**************
Franco Ventriglia (Napoli)
Transformation properties of generalized Wigner
functions on Weyl-Heisenberg group
A
natural extension of the Wigner function on the space of irreducible unitary
representations of the Weyl-Heisenberg group is discussed. The action of the
automorphism group of the Weyl-Heisenberg group onto Wigner functions and
their generalizations and onto symplectic tomograms is elucidated. Some
examples of physical systems are considered to illustrate some aspects of the
characterization of the Wigner functions as solutions of differential
equations.
*************
Kazuya YUASA (Waseda
University, Tokyo)
Entanglement Generation by Scattering an Ancillary
Qubit in 3D
A
scheme for generating an entangled state in two qubits by means of a
spin-dependent potential scattering of another qubit is presented and
analyzed in 3D space. Several features such as the incident and scattering
angles, the size of the mouth of the detector, and the size of the incident
wave packet affect the degree of the entanglement to be generated. All the
characteristics are understandable in terms of the indistinguishability of
the path of the scattered qubit. The full order
calculation to take account of the multiple scatterings between
the two qubits requires an appropriate renormalization of delta-shaped
potentials in 3D space.
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