753 research outputs found
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
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
The optimal cloning of quantum coherent states is non-Gaussian
We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.Comment: 4 pages, 2 figures, revtex; changed title, extended list of authors,
included optical implementation of optimal clone
Homodyne locking of a squeezer
We report on the successful implementation of a new approach to locking the
frequencies of an OPO-based squeezed-vacuum source and its driving laser. The
technique allows the simultaneous measurement of the phase-shifts induced by a
cavity, which may be used for the purposes of frequency-locking, as well as the
simultaneous measurement of the sub-quantum-noise-limited (sub-QNL) phase
quadrature output of the OPO. The homodyne locking technique is cheap, easy to
implement and has the distinct advantage that subsequent homodyne measurements
are automatically phase-locked. The homodyne locking technique is also unique
in that it is a sub-QNL frequency discriminator.Comment: Accepted to Optics Letter
Experimental quantum key distribution over highly noisy channels
Error filtration is a method for encoding the quantum state of a single
particle into a higher dimensional Hilbert space in such a way that it becomes
less sensitive to phase noise. We experimentally demonstrate this method by
distributing a secret key over an optical fiber whose noise level otherwise
precludes secure quantum key distribution. By filtering out the phase noise, a
bit error rate of 15.3% +/- 0.1%, which is beyond the security limit, can be
reduced to 10.6% +/- 0.1%, thereby guaranteeing the cryptographic security.Comment: 4 pages, 2 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.
Optimal N-to-M Cloning of Quantum Coherent States
The cloning of continuous quantum variables is analyzed based on the concept
of Gaussian cloning machines, i.e., transformations that yield copies that are
Gaussian mixtures centered on the state to be copied. The optimality of
Gaussian cloning machines that transform N identical input states into M output
states is investigated, and bounds on the fidelity of the process are derived
via a connection with quantum estimation theory. In particular, the optimal
N-to-M cloning fidelity for coherent states is found to be equal to
MN/(MN+M-N).Comment: 3 pages, RevTe
"Squashed Entanglement" - An Additive Entanglement Measure
In this paper, we present a new entanglement monotone for bipartite quantum
states. Its definition is inspired by the so-called intrinsic information of
classical cryptography and is given by the halved minimum quantum conditional
mutual information over all tripartite state extensions. We derive certain
properties of the new measure which we call "squashed entanglement": it is a
lower bound on entanglement of formation and an upper bound on distillable
entanglement. Furthermore, it is convex, additive on tensor products, and
superadditive in general.
Continuity in the state is the only property of our entanglement measure
which we cannot provide a proof for. We present some evidence, however, that
our quantity has this property, the strongest indication being a conjectured
Fannes type inequality for the conditional von Neumann entropy. This inequality
is proved in the classical case.Comment: 8 pages, revtex4. v2 has some more references and a bit more
discussion, v3 continuity discussion extended, typos correcte
Continuous variable quantum cryptography using coherent states
We propose several methods for quantum key distribution (QKD) based upon the
generation and transmission of random distributions of coherent or squeezed
states, and we show that they are are secure against individual eavesdropping
attacks. These protocols require that the transmission of the optical line
between Alice and Bob is larger than 50 %, but they do not rely on
"non-classical" features such as squeezing. Their security is a direct
consequence of the no-cloning theorem, that limits the signal to noise ratio of
possible quantum measurements on the transmission line. Our approach can also
be used for evaluating various QKD protocols using light with gaussian
statistics.Comment: 5 pages, 1 figure. In v2 minor rewriting for clarity, references
adde
A probabilistic phase-insensitive optical squeezer in peaceful coexistence with causality
A non trace-preserving map describing a probabilistic but heralded noiseless
linear amplifier has recently been proposed and experimentally demonstrated.
Here, we exhibit another remarkable feature of this peculiar transformation,
namely its ability to serve as a universal single-mode squeezer regardless of
the quadrature that is initially squeezed. Hence, it acts as an heralded
phase-insensitive optical squeezer, conserving the signal-to-noise ratio just
as a phase-sensitive optical amplifier but for all quadratures at the same
time, which may offer new perspectives in quantum optical communications.
Although this ability to squeeze all quadratures seemingly opens a way to
instantaneous signaling by circumventing the quantum no-cloning theorem, we
explain the subtle mechanism by which the probability for such a causality
violation vanishes, even on an heralded basis
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