15 research outputs found
Evanescence in coined quantum walks
In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105]. We obtain uniformly convergent asymptotics for the exponential decay regions at the leading edges of the main peaks in the Sch
Normal forms and entanglement measures for multipartite quantum states
A general mathematical framework is presented to describe local equivalence
classes of multipartite quantum states under the action of local unitary and
local filtering operations. This yields multipartite generalizations of the
singular value decomposition. The analysis naturally leads to the introduction
of entanglement measures quantifying the multipartite entanglement (as
generalizations of the concurrence and the 3-tangle), and the optimal local
filtering operations maximizing these entanglement monotones are obtained.
Moreover a natural extension of the definition of GHZ-states to e.g. systems is obtained.Comment: Proof of uniqueness of normal form adde
Constraint on teleportation over multipartite pure states
We first define a quantity exhibiting the usefulness of bipartite quantum
states for teleportation, called the quantum teleportation capability, and then
investigate its restricted shareability in multi-party quantum systems. In this
work, we verify that the quantum teleportation capability has a monogamous
property in its shareability for arbitrary three-qutrit pure states by
employing the monogamy inequality in terms of the negativity.Comment: 4 pages, 1 figur
Geometry of entangled states
Geometric properties of the set of quantum entangled states are investigated.
We propose an explicit method to compute the dimension of local orbits for any
mixed state of the general K x M problem and characterize the set of
effectively different states (which cannot be related by local
transformations). Thus we generalize earlier results obtained for the simplest
2 x 2 system, which lead to a stratification of the 6D set of N=4 pure states.
We define the concept of absolutely separable states, for which all globally
equivalent states are separable.Comment: 16 latex pages, 4 figures in epsf, minor corrections, references
updated, to appear in Phys. Rev.
Classification of multipartite entangled states by multidimensional determinants
We find that multidimensional determinants "hyperdeterminants", related to
entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3
qubits, respectively), are derived from a duality between entangled states and
separable states. By means of the hyperdeterminant and its singularities, the
single copy of multipartite pure entangled states is classified into an onion
structure of every closed subset, similar to that by the local rank in the
bipartite case. This reveals how inequivalent multipartite entangled classes
are partially ordered under local actions. In particular, the generic entangled
class of the maximal dimension, distinguished as the nonzero hyperdeterminant,
does not include the maximally entangled states in Bell's inequalities in
general (e.g., in the qubits), contrary to the widely known
bipartite or 3-qubit cases. It suggests that not only are they never locally
interconvertible with the majority of multipartite entangled states, but they
would have no grounds for the canonical n-partite entangled states. Our
classification is also useful for the mixed states.Comment: revtex4, 10 pages, 4 eps figures with psfrag; v2 title changed, 1
appendix added, to appear in Phys. Rev.
Generalised quantum weakest preconditions
Generalisation of the quantum weakest precondition result of D'Hondt and
Panangaden is presented. In particular the most general notion of quantum
predicate as positive operator valued measure (POVM) is introduced. The
previously known quantum weakest precondition result has been extended to cover
the case of POVM playing the role of a quantum predicate. Additionally, our
result is valid in infinite dimension case and also holds for a quantum
programs defined as a positive but not necessary completely positive
transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten
Classification of qubit entanglement: SL(2,C) versus SU(2) invariance
The role of SU(2) invariants for the classification of multiparty
entanglement is discussed and exemplified for the Kempe invariant I_5 of pure
three-qubit states. It is found to being an independent invariant only in
presence of both W-type entanglement and threetangle. In this case, constant
I_5 admits for a wide range of both threetangle and concurrences. Furthermore,
the present analysis indicates that an SL^3 orbit of states with equal tangles
but continuously varying I_5 must exist. This means that I_5 provides no
information on the entanglement in the system in addition to that contained in
the tangles (concurrences and threetangle) themselves. Together with the
numerical evidence that I_5 is an entanglement monotone this implies that SU(2)
invariance or the monotone property are too weak requirements for the
characterization and quantification of entanglement for systems of three
qubits, and that SL(2,C) invariance is required. This conclusion can be
extended to general multipartite systems (including higher local dimension)
because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex
Generation of maximum spin entanglement induced by cavity field in quantum-dot systems
Equivalent-neighbor interactions of the conduction-band electron spins of
quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)]
are analyzed. Analytical solution and its Schmidt decomposition are found and
applied to evaluate how much the initially excited dots can be entangled to the
remaining dots if all of them are initially disentangled. It is demonstrated
that the perfect maximally entangled states (MES) can only be generated in the
systems of up to 6 dots with a single dot initially excited. It is also shown
that highly entangled states, approximating the MES with a good accuracy, can
still be generated in systems of odd number of dots with almost half of them
being excited. A sudden decrease of entanglement is observed by increasing the
total number of dots in a system with a fixed number of excitations.Comment: 6 pages, 7 figures, to appear in Phys. Rev.
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa