14 research outputs found
On the Phase Covariant Quantum Cloning
It is known that in phase covariant quantum cloning the equatorial states on
the Bloch sphere can be cloned with a fidelity higher than the optimal bound
established for universal quantum cloning. We generalize this concept to
include other states on the Bloch sphere with a definite component of spin.
It is shown that once we know the component, we can always clone a state
with a fidelity higher than the universal value and that of equatorial states.
We also make a detailed study of the entanglement properties of the output
copies and show that the equatorial states are the only states which give rise
to separable density matrix for the outputs.Comment: Revtex4, 6 pages, 5 eps figure
Quantum Cloning Machines of a d-level System
The optimal N to M () quantum cloning machines for the d-level system
are presented. The unitary cloning transformations achieve the bound of the
fidelity.Comment: Revtex, 4 page
Separability and distillability in composite quantum systems -a primer-
Quantum mechanics is already 100 years old, but remains alive and full of
challenging open problems. On one hand, the problems encountered at the
frontiers of modern theoretical physics like Quantum Gravity, String Theories,
etc. concern Quantum Theory, and are at the same time related to open problems
of modern mathematics. But even within non-relativistic quantum mechanics
itself there are fundamental unresolved problems that can be formulated in
elementary terms. These problems are also related to challenging open questions
of modern mathematics; linear algebra and functional analysis in particular.
Two of these problems will be discussed in this article: a) the separability
problem, i.e. the question when the state of a composite quantum system does
not contain any quantum correlations or entanglement and b) the distillability
problem, i.e. the question when the state of a composite quantum system can be
transformed to an entangled pure state using local operations (local refers
here to component subsystems of a given system).
Although many results concerning the above mentioned problems have been
obtained (in particular in the last few years in the framework of Quantum
Information Theory), both problems remain until now essentially open. We will
present a primer on the current state of knowledge concerning these problems,
and discuss the relation of these problems to one of the most challenging
questions of linear algebra: the classification and characterization of
positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod.
Optics, minor typos corrected, references adde
Differential Geometry of Bipartite Quantum States
We investigate the differential geometry of bipartite quantum states. In
particular the manifold structures of pure bipartite states are studied in
detail. The manifolds with respect to all normalized pure states of arbitrarily
given Schmidt ranks or Schmidt coefficients are explicitly presented. The
dimensions of the related manifolds are calculated.Comment: 10 page
Theoretical efficient high capacity Quantum Key Distribution Scheme
A theoretical quantum key distribution scheme using EPR pairs is presented.
This scheme is efficient in that it uses all EPR pairs in distributing the key
except those chosen for checking eavesdroppers. The high capacity is achieved
because each EPR pair carries 2 bits of key code.Comment: 3 pages and 1 figure, to appear in Physical Review
Entanglement in a simple quantum phase transition
What entanglement is present in naturally occurring physical systems at
thermal equilibrium? Most such systems are intractable and it is desirable to
study simple but realistic systems which can be solved. An example of such a
system is the 1D infinite-lattice anisotropic XY model. This model is exactly
solvable using the Jordan-Wigner transform, and it is possible to calculate the
two-site reduced density matrix for all pairs of sites. Using the two-site
density matrix, the entanglement of formation between any two sites is
calculated for all parameter values and temperatures. We also study the
entanglement in the transverse Ising model, a special case of the XY model,
which exhibits a quantum phase transition. It is found that the next-nearest
neighbour entanglement (though not the nearest-neighbour entanglement) is a
maximum at the critical point. Furthermore, we show that the critical point in
the transverse Ising model corresponds to a transition in the behaviour of the
entanglement between a single site and the remainder of the lattice.Comment: 14 pages, 7 eps figure