23,452 research outputs found
A universal quantum circuit for two-qubit transformations with three CNOT gates
We consider the implementation of two-qubit unitary transformations by means
of CNOT gates and single-qubit unitary gates. We show, by means of an explicit
quantum circuit, that together with local gates three CNOT gates are necessary
and sufficient in order to implement an arbitrary unitary transformation of two
qubits. We also identify the subset of two-qubit gates that can be performed
with only two CNOT gates.Comment: 3 pages, 7 figures. One theorem, one author and references added.
Change of notational conventions. Minor correction in Theorem
Optimal distillation of a GHZ state
We present the optimal local protocol to distill a
Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of
three qubits.Comment: RevTex, 4 pages, 2 figures. Published version, some references adde
Simulation of anyons with tensor network algorithms
Interacting systems of anyons pose a unique challenge to condensed matter
simulations due to their non-trivial exchange statistics. These systems are of
great interest as they have the potential for robust universal quantum
computation, but numerical tools for studying them are as yet limited. We show
how existing tensor network algorithms may be adapted for use with systems of
anyons, and demonstrate this process for the 1-D Multi-scale Entanglement
Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of
interacting Fibonacci anyons, computing their scaling dimensions and local
scaling operators. The scaling dimensions obtained are seen to be in agreement
with conformal field theory. The techniques developed are applicable to any
tensor network algorithm, and the ability to adapt these ansaetze for use on
anyonic systems opens the door for numerical simulation of large systems of
free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4
tables, RevTeX 4-1. For a related work, see arXiv:1006.247
Optimal entanglement manipulation via coherent-state transmission
We derive an optimal bound for arbitrary entanglement manipulation based on
the transmission of a pulse in coherent states over a lossy channel followed by
local operations and unlimited classical communication (LOCC). This stands on a
theorem to reduce LOCC via a local unital qubit channel to local filtering. We
also present an optimal protocol based on beam splitters and a quantum
nondemolition (QND) measurement on photons. Even if we replace the QND
measurement with photon detectors, the protocol outperforms known entanglement
generation schemes.Comment: 5 pages, 1 figur
Optimal quantum teleportation with an arbitrary pure state
We derive the maximum fidelity attainable for teleportation using a shared
pair of d-level systems in an arbitrary pure state. This derivation provides a
complete set of necessary and sufficient conditions for optimal teleportation
protocols. We also discuss the information on the teleported particle which is
revealed in course of the protocol using a non-maximally entangled state.Comment: 10 pages, REVTe
Entanglement cost of mixed states
We compute the entanglement cost of several families of bipartite mixed
states, including arbitrary mixtures of two Bell states. This is achieved by
developing a technique that allows us to ascertain the additivity of the
entanglement of formation for any state supported on specific subspaces. As a
side result, the proof of the irreversibility in asymptotic local manipulations
of entanglement is extended to two-qubit systems.Comment: 4 pages, no figures, (v4) new results, including a new method to
determine E_c for more general mixed states, presentation changed
significantl
Non-local scaling operators with entanglement renormalization
The multi-scale entanglement renormalization ansatz (MERA) can be used, in
its scale invariant version, to describe the ground state of a lattice system
at a quantum critical point. From the scale invariant MERA one can determine
the local scaling operators of the model. Here we show that, in the presence of
a global symmetry , it is also possible to determine a class of
non-local scaling operators. Each operator consist, for a given group element
, of a semi-infinite string \tGamma_g with a local operator
attached to its open end. In the case of the quantum Ising model,
, they correspond to the disorder operator ,
the fermionic operators and , and all their descendants.
Together with the local scaling operators identity , spin
and energy , the fermionic and disorder scaling operators ,
and are the complete list of primary fields of the Ising
CFT. Thefore the scale invariant MERA allows us to characterize all the
conformal towers of this CFT.Comment: 4 pages, 4 figures. Revised versio
Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
We propose the concept of SLOCC-equivalent basis (SEB) in the multiqubit
space. In particular, two special SEBs, the GHZ-type and the W-type basis are
introduced. They can make up a more general family of multiqubit states, the
GHZ-W-type states, which is a useful kind of entanglement for quantum
teleporatation and error correction. We completely characterize the property of
this type of states, and mainly classify the GHZ-type states and the W-type
states in a regular way, which is related to the enumerative combinatorics.
Many concrete examples are given to exhibit how our method is used for the
classification of these entangled states.Comment: 16 pages, Revte
Mixed State Entanglement of Assistance and the Generalized Concurrence
We consider the maximum bipartite entanglement that can be distilled from a
single copy of a multipartite mixed entangled state, where we focus mostly on
-dimensional tripartite mixed states. We show that this {\em
assisted entanglement}, when measured in terms of the generalized concurrence
(named G-concurrence) is (tightly) bounded by an entanglement monotone, which
we call the G-concurrence of assistance. The G-concurrence is one of the
possible generalizations of the concurrence to higher dimensions, and for pure
bipartite states it measures the {\em geometric mean} of the Schmidt numbers.
For a large (non-trivial) class of -dimensional mixed states, we are
able to generalize Wootters formula for the concurrence into lower and upper
bounds on the G-concurrence. Moreover, we have found an explicit formula for
the G-concurrence of assistance that generalizes the expression for the
concurrence of assistance for a large class of dimensional
tripartite pure states.Comment: 7 page
Low energy excitations of the kagome antiferromagnet and the spin gap issue
In this paper we report the latest results of exact diagonalizations of SU(2)
invariant models on various lattices (square, triangular, hexagonal,
checkerboard and kagome lattices). We focus on the low lying levels in each S
sector. The differences in behavior between gapless systems and gapped ones are
exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on
the kagome lattice is discussed. A rough estimate of the spin susceptibility in
such an hypothesis is given.The evolution of the intra-S channel spectra under
the effect of a small perturbation is consistent with the proximity of a
quantum critical point. We emphasize that the very small intra-S channel energy
scale observed in exact spectra is a very interesting information to understand
the low T dynamics of this model.Comment: 6 pages, 5 figures, revised version with a more extended discussion
on the issue of a possible proximity with a quantum critical point, a few
more details and references, a modified Fig
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