932 research outputs found
Cloning quantum entanglement in arbitrary dimensions
We have found a quantum cloning machine that optimally duplicates the
entanglement of a pair of -dimensional quantum systems. It maximizes the
entanglement of formation contained in the two copies of any
maximally-entangled input state, while preserving the separability of
unentangled input states. Moreover, it cannot increase the entanglement of
formation of all isotropic states. For large , the entanglement of formation
of each clone tends to one half the entanglement of the input state, which
corresponds to a classical behavior. Finally, we investigate a local
entanglement cloner, which yields entangled clones with one fourth the input
entanglement in the large- limit.Comment: 6 pages, 3 figure
Monte Carlo Simulation of Quantum Computation
The many-body dynamics of a quantum computer can be reduced to the time
evolution of non-interacting quantum bits in auxiliary fields by use of the
Hubbard-Stratonovich representation of two-bit quantum gates in terms of
one-bit gates. This makes it possible to perform the stochastic simulation of a
quantum algorithm, based on the Monte Carlo evaluation of an integral of
dimension polynomial in the number of quantum bits. As an example, the
simulation of the quantum circuit for the Fast Fourier Transform is discussed.Comment: 12 pages Latex, 2 Postscript figures, to appear in Proceedings of the
IMACS (International Association for Mathematics and Computers in Simulation)
Conference on Monte Carlo Methods, Brussels, April 9
Optimal cloning of mixed Gaussian states
We construct the optimal 1 to 2 cloning transformation for the family of
displaced thermal equilibrium states of a harmonic oscillator, with a fixed and
known temperature. The transformation is Gaussian and it is optimal with
respect to the figure of merit based on the joint output state and norm
distance. The proof of the result is based on the equivalence between the
optimal cloning problem and that of optimal amplification of Gaussian states
which is then reduced to an optimization problem for diagonal states of a
quantum oscillator. A key concept in finding the optimum is that of stochastic
ordering which plays a similar role in the purely classical problem of Gaussian
cloning. The result is then extended to the case of n to m cloning of mixed
Gaussian states.Comment: 8 pages, 1 figure; proof of general form of covariant amplifiers
adde
Quantum conditional operator and a criterion for separability
We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
, where is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
and systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.Comment: 19 pages, RevTe
Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm
We analyze three different quantum search algorithms, the traditional
Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and
finally the quantum search by local adiabatic evolution. We show that they are
closely related algorithms in the sense that they all perform a rotation, at a
constant angular velocity, from a uniform superposition of all states to the
solution state. This make it possible to implement the last two algorithms by
Hamiltonian evolution on a conventional quantum circuit, while keeping the
quadratic speedup of Grover's original algorithm.Comment: 5 pages, 3 figure
What information theory can tell us about quantum reality
An investigation of Einstein's ``physical'' reality and the concept of
quantum reality in terms of information theory suggests a solution to quantum
paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat
paradoxes. Quantum reality, the picture based on unitarily evolving
wavefunctions, is complete, but appears incomplete from the observer's point of
view for fundamental reasons arising from the quantum information theory of
measurement. Physical reality, the picture based on classically accessible
observables is, in the worst case of EPR experiments, unrelated to the quantum
reality it purports to reflect. Thus, quantum information theory implies that
only correlations, not the correlata, are physically accessible: the mantra of
the Ithaca interpretation of quantum mechanics.Comment: LaTeX with llncs.cls, 11 pages, 6 postscript figures, Proc. of 1st
NASA Workshop on Quantum Computation and Quantum Communication (QCQC 98
On the formation/dissolution of equilibrium droplets
We consider liquid-vapor systems in finite volume at parameter
values corresponding to phase coexistence and study droplet formation due to a
fixed excess of particles above the ambient gas density. We identify
a dimensionless parameter and a
\textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the
dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the
excess is entirely absorbed into the gaseous background. When the droplet first
forms, it comprises a non-trivial, \textrm{universal} fraction of excess
particles. Similar reasoning applies to generic two-phase systems at phase
coexistence including solid/gas--where the ``droplet'' is crystalline--and
polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas
is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model;
to appear in Europhys. Let
Hybrid Qubit gates in circuit QED: A scheme for quantum bit encoding and information processing
Solid state superconducting devices coupled to coplanar transmission lines
offer an exquisite architecture for quantum optical phenomena probing as well
as for quantum computation implementation, being the object of intense
theoretical and experimental investigation lately. In appropriate conditions
the transmission line radiation modes can get strongly coupled to a
superconducting device with only two levels -for that reason called artificial
atom or qubit. Employing this system we propose a hybrid two-quantum bit gate
encoding involving quantum electromagnetic field qubit states prepared in a
coplanar transmission line capacitively coupled to a single charge qubit. Since
dissipative effects are more drastic in the solid state qubit than in the field
one, it can be employed for storage of information, whose efficiency against
the action of an ohmic bath show that this encoding can be readily implemented
with present day technology. We extend the investigation to generate
entanglement between several solid state qubits and the field qubit through the
action of external classical magnetic pulses.Comment: 9 pages, 10 figure
Entanglement may enhance the channel capacity in arbitrary dimensions
We consider explicitly two examples of d-dimensional quantum channels with
correlated noise and show that, in agreement with previous results on Pauli
qubit channels, there are situations where maximally entangled input states
achieve higher values of the output mutual information than product states. We
obtain a strong dependence of this effect on the nature of the noise
correlations as well as on the parity of the space dimension, and conjecture
that when entanglement gives an advantage in terms of mutual information,
maximally entangled states achieve the channel capacity.Comment: 12 pages, 3 figure
Information-theoretic interpretation of quantum error-correcting codes
Quantum error-correcting codes are analyzed from an information-theoretic
perspective centered on quantum conditional and mutual entropies. This approach
parallels the description of classical error correction in Shannon theory,
while clarifying the differences between classical and quantum codes. More
specifically, it is shown how quantum information theory accounts for the fact
that "redundant" information can be distributed over quantum bits even though
this does not violate the quantum "no-cloning" theorem. Such a remarkable
feature, which has no counterpart for classical codes, is related to the
property that the ternary mutual entropy vanishes for a tripartite system in a
pure state. This information-theoretic description of quantum coding is used to
derive the quantum analogue of the Singleton bound on the number of logical
bits that can be preserved by a code of fixed length which can recover a given
number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in
Phys. Rev.
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