1,059 research outputs found
Local symmetry properties of pure 3-qubit states
Entanglement types of pure states of 3 qubits are classified by means of
their stabilisers in the group of local unitary operations. It is shown that
the stabiliser is generically discrete, and that a larger stabiliser indicates
a stationary value for some local invariant. We describe all the exceptional
states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published
version, with minor correction
Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
Two random-walk related problems which have been studied independently in the
past, the expected maximum of a random walker in one dimension and the flux to
a spherical trap of particles undergoing discrete jumps in three dimensions,
are shown to be closely related to each other and are studied using a unified
approach as a solution to a Wiener-Hopf problem. For the flux problem, this
work shows that a constant c = 0.29795219 which appeared in the context of the
boundary extrapolation length, and was previously found only numerically, can
be derived explicitly. The same constant enters in higher-order corrections to
the expected-maximum asymptotics. As a byproduct, we also prove a new universal
result in the context of the flux problem which is an analogue of the Sparre
Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic
Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
We investigate the entanglement between any two spins in a one dimensional
Heisenberg chain as a function of temperature and the external magnetic field.
We find that the entanglement in an antiferromagnetic chain can be increased by
increasing the temperature or the external field. Increasing the field can also
create entanglement between otherwise disentangled spins. This entanglement can
be confirmed by testing Bell's inequalities involving any two spins in the
solid.Comment: 4 pages, 5 figure
Parallel transport in an entangled ring
This paper defines a notion of parallel transport in a lattice of quantum
particles, such that the transformation associated with each link of the
lattice is determined by the quantum state of the two particles joined by that
link. We focus particularly on a one-dimensional lattice--a ring--of entangled
rebits, which are binary quantum objects confined to a real state space. We
consider states of the ring that maximize the correlation between nearest
neighbors, and show that some correlation must be sacrificed in order to have
non-trivial parallel transport around the ring. An analogy is made with lattice
gauge theory, in which non-trivial parallel transport around closed loops is
associated with a reduction in the probability of the field configuration. We
discuss the possibility of extending our result to qubits and to higher
dimensional lattices.Comment: 31 pages, no figures; v2 includes a new example of a qubit rin
Quantum cobwebs: Universal entangling of quantum states
Entangling an unknown qubit with one type of reference state is generally
impossible. However, entangling an unknown qubit with two types of reference
states is possible. To achieve this, we introduce a new class of states called
zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and
study their salient features. Using shared-ZSA state, local operation and
classical communication we give a protocol for creating multipartite entangled
states of an unknown quantum state with two types of reference states at remote
places. This provides a way of encoding an unknown pure qubit state into a
multiqubit entangled state. We quantify the amount of classical and quantum
resources required to create universal entangled states. This is possibly a
strongest form of quantum bit hiding with multiparties.Comment: Invited talk in II Winter Institute on FQTQO: Quantum Information
Processing, held at S. N. Bose Center for Basic Science, Kolkata, during Jan
2-11, 2002. (To appear in Pramana-J. of Physics, 2002.
A bipartite class of entanglement monotones for N-qubit pure states
We construct a class of algebraic invariants for N-qubit pure states based on
bipartite decompositions of the system.
We show that they are entanglement monotones, and that they differ from the
well know linear entropies of the sub-systems. They therefore capture new
information on the non-local properties of multipartite systems.Comment: 6 page
Entangled Rings
Consider a ring of N qubits in a translationally invariant quantum state. We
ask to what extent each pair of nearest neighbors can be entangled. Under
certain assumptions about the form of the state, we find a formula for the
maximum possible nearest-neighbor entanglement. We then compare this maximum
with the entanglement achieved by the ground state of an antiferromagnetic ring
consisting of an even number of spin-1/2 particles. We find that, though the
antiferromagnetic ground state does not maximize the nearest-neighbor
entanglement relative to all other states, it does so relative to other states
having zero z-component of spin.Comment: 19 pages, no figures; v2 includes new results; v3 corrects a
numerical error for the case N=
Three-qubit pure-state canonical forms
In this paper we analyze the canonical forms into which any pure three-qubit
state can be cast. The minimal forms, i.e. the ones with the minimal number of
product states built from local bases, are also presented and lead to a
complete classification of pure three-qubit states. This classification is
related to the values of the polynomial invariants under local unitary
transformations by a one-to-one correspondence.Comment: REVTEX, 9 pages, 1 figur
Distributed Entanglement
Consider three qubits A, B, and C which may be entangled with each other. We
show that there is a trade-off between A's entanglement with B and its
entanglement with C. This relation is expressed in terms of a measure of
entanglement called the "tangle," which is related to the entanglement of
formation. Specifically, we show that the tangle between A and B, plus the
tangle between A and C, cannot be greater than the tangle between A and the
pair BC. This inequality is as strong as it could be, in the sense that for any
values of the tangles satisfying the corresponding equality, one can find a
quantum state consistent with those values. Further exploration of this result
leads to a definition of the "three-way tangle" of the system, which is
invariant under permutations of the qubits.Comment: 13 pages LaTeX; references added, derivation of Eq. (11) simplifie
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