288 research outputs found
Quantum state engineering, purification, and number resolved photon detection with high finesse optical cavities
We propose and analyze a multi-functional setup consisting of high finesse
optical cavities, beam splitters, and phase shifters. The basic scheme projects
arbitrary photonic two-mode input states onto the subspace spanned by the
product of Fock states |n>|n> with n=0,1,2,.... This protocol does not only
provide the possibility to conditionally generate highly entangled photon
number states as resource for quantum information protocols but also allows one
to test and hence purify this type of quantum states in a communication
scenario, which is of great practical importance. The scheme is especially
attractive as a generalization to many modes allows for distribution and
purification of entanglement in networks. In an alternative working mode, the
setup allows of quantum non demolition number resolved photodetection in the
optical domain.Comment: 14 pages, 10 figure
On the fidelity of two pure states
The fidelity of two pure states (also known as transition probability) is a
symmetric function of two operators, and well-founded operationally as an event
probability in a certain preparation-test pair. Motivated by the idea that the
fidelity is the continuous quantum extension of the combinatorial equality
function, we enquire whether there exists a symmetric operational way of
obtaining the fidelity. It is shown that this is impossible. Finally, we
discuss the optimal universal approximation by a quantum operation.Comment: LaTeX2e, 8 pages, submitted to J. Phys. A: Math. and Ge
On 1-qubit channels
The entropy H_T(rho) of a state rho with respect to a channel T and the
Holevo capacity of the channel require the solution of difficult variational
problems. For a class of 1-qubit channels, which contains all the extremal
ones, the problem can be significantly simplified by associating an Hermitian
antilinear operator theta to every channel of the considered class. The
concurrence of the channel can be expressed by theta and turns out to be a flat
roof. This allows to write down an explicit expression for H_T. Its maximum
would give the Holevo (1-shot) capacity.Comment: 12 pages, several printing or latex errors correcte
Entanglement Measures under Symmetry
We show how to simplify the computation of the entanglement of formation and
the relative entropy of entanglement for states, which are invariant under a
group of local symmetries. For several examples of groups we characterize the
state spaces, which are invariant under these groups. For specific examples we
calculate the entanglement measures. In particular, we derive an explicit
formula for the entanglement of formation for UU-invariant states, and we find
a counterexample to the additivity conjecture for the relative entropy of
entanglement.Comment: RevTeX,16 pages,9 figures, reference added, proof of monotonicity
corrected, results unchange
Tripartite entanglement and quantum relative entropy
We establish relations between tripartite pure state entanglement and
additivity properties of the bipartite relative entropy of entanglement. Our
results pertain to the asymptotic limit of local manipulations on a large
number of copies of the state. We show that additivity of the relative entropy
would imply that there are at least two inequivalent types of asymptotic
tripartite entanglement. The methods used include the application of some
useful lemmas that enable us to analytically calculate the relative entropy for
some classes of bipartite states.Comment: 7 pages, revtex, no figures. v2: discussion about recent results, 2
refs. added. Published versio
All Teleportation and Dense Coding Schemes
We establish a one-to-one correspondence between (1) quantum teleportation
schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled
vectors, (4) orthonormal bases of unitary operators with respect to the
Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus
operators can be chosen to be unitary. The teleportation and dense coding
schemes are assumed to be ``tight'' in the sense that all Hilbert spaces
involved have the same finite dimension d, and the classical channel involved
distinguishes d^2 signals. A general construction procedure for orthonormal
bases of unitaries, involving Latin Squares and complex Hadamard Matrices is
also presented.Comment: 21 pages, LaTe
Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
The set of doubly-stochastic quantum channels and its subset of mixtures of
unitaries are investigated. We provide a detailed analysis of their structure
together with computable criteria for the separation of the two sets. When
applied to O(d)-covariant channels this leads to a complete characterization
and reveals a remarkable feature: instances of channels which are not in the
convex hull of unitaries can return to it when either taking finitely many
copies of them or supplementing with a completely depolarizing channel. In
these scenarios this implies that a channel whose noise initially resists any
environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page
Conditional q-Entropies and Quantum Separability: A Numerical Exploration
We revisit the relationship between quantum separability and the sign of the
relative q-entropies of composite quantum systems. The q-entropies depend on
the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q.
Renyi's and Tsallis' measures constitute particular instances of these
entropies. We perform a systematic numerical survey of the space of mixed
states of two-qubit systems in order to determine, as a function of the degree
of mixture, and for different values of the entropic parameter q, the volume in
state space occupied by those states characterized by positive values of the
relative entropy. Similar calculations are performed for qubit-qutrit systems
and for composite systems described by Hilbert spaces of larger dimensionality.
We pay particular attention to the limit case q --> infinity. Our numerical
results indicate that, as the dimensionalities of both subsystems increase,
composite quantum systems tend, as far as their relative q-entropies are
concerned, to behave in a classical way
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