27 research outputs found
Fast rate estimation of an unitary operation in SU(d)
We give an explicit procedure based on entangled input states for estimating
a operation with rate of convergence when sending
particles through the device. We prove that this rate is optimal. We also
evaluate the constant such that the asymptotic risk is . However
other strategies might yield a better const ant .Comment: 8 pages, 1 figure Rewritten version, accepted for publication in
Phys. Rev. A. The introduction is richer, the "tool section" on group
representations has been suppressed, and a section proving that the 1/N^2
rate is optimum has been adde
All maximally entangling unitary gates
We characterize all maximally entangling bipartite unitary operators, acting
on systems of arbitrary finite dimensions , when use of
ancillary systems by both parties is allowed. Several useful and interesting
consequences of this characterization are discussed, including an understanding
of why the entangling and disentangling capacities of a given (maximally
entangling) unitary can differ and a proof that these capacities must be equal
when .Comment: 7 pages, no figure
Hermitian Young Operators
Starting from conventional Young operators we construct Hermitian operators
which project orthogonally onto irreducible representations of the (special)
unitary group.Comment: 15 page
Optimizing local protocols implementing nonlocal quantum gates
We present a method of optimizing recently designed protocols for
implementing an arbitrary nonlocal unitary gate acting on a bipartite system.
These protocols use only local operations and classical communication with the
assistance of entanglement, and are deterministic while also being "one-shot",
in that they use only one copy of an entangled resource state. The optimization
is in the sense of minimizing the amount of entanglement used, and it is often
the case that less entanglement is needed than with an alternative protocol
using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546
Solution of the infinite range t-J model
The t-J model with constant t and J between any pair of sites is studied by
exploiting the symmetry of the Hamiltonian with respect to site permutations.
For a given number of electrons and a given total spin the exchange term simply
yields an additive constant. Therefore the real problem is to diagonalize the
"t- model", or equivalently the infinite U Hubbard Hamiltonian. Using
extensively the properties of the permutation group, we are able to find
explicitly both the energy eigenvalues and eigenstates, labeled according to
spin quantum numbers and Young diagrams. As a corollary we also obtain the
degenerate ground states of the finite Hubbard model with infinite range
hopping -t>0.Comment: 15 pages, 2 figure
Expected length of the longest common subsequence for large alphabets
We consider the length L of the longest common subsequence of two randomly
uniformly and independently chosen n character words over a k-ary alphabet.
Subadditivity arguments yield that the expected value of L, when normalized by
n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville
from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe
Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models
We study a generalized multichannel single-impurity Kondo model, in which the
impurity spin is described by a representation of the SU(N) group which
combines bosonic and fermionic degrees of freedom. The impurity spin states are
described by Abrikosov pseudofermions, and we make use of a method initiated by
Popov and Fedotov which allows a proper handling of the fermionic constraint.
The partition function is derived within a path integral approach. We use
renormalization group techniques to calculate the scaling function
perturbatively in powers of the Kondo coupling constant, which is justified in
the weak coupling limit. The truncated expansion is valid in the overscreened
(Nozieres-Blandin) regime, for an arbitrary SU(N) group and any value of the
parameters characterizing the impurity spin representation. The intermediate
coupling fixed point is identified. We derive the temperature dependence of
various physical quantities at low T, controlled by a unique critical exponent,
and show that the physics of the system in the overscreened regime governed by
the intermediate coupling fixed point is characterized by a non-Fermi liquid
behavior. Our results are in accordance with those obtained by other methods,
as Bethe ansatz and boundary conformal field theory, in the case of various
impurity spin symmetries. We establish in a unified way that the Kondo models
in which the impurity spin is described successively by a fundamental,
symmetric, antisymmetric and mixed symmetry representation yield all the same
low-energy physics in the overscreened regime. Possible generalizations of the
analysis we present to the case of arbitrary impurity spin representations of
SU(N) are also discussed.Comment: 21 pages, 7 figures, REVTeX; final version accepted for publicatio
Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors
The exchange interaction between identical qubits in a quantum information
processor gives rise to unitary two-qubit errors. It is shown here that
decoherence free subspaces (DFSs) for collective decoherence undergo Pauli
errors under exchange, which however do not take the decoherence free states
outside of the DFS. In order to protect DFSs against these errors it is
sufficient to employ a recently proposed concatenated DFS-quantum error
correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett.
{\bf 82}, 4556 (1999)].Comment: 7 pages, no figures. Discussion in section V.A. significantly
expanded. Several small changes. Two authors adde
Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
Coherence in an open quantum system is degraded through its interaction with
a bath. This decoherence can be avoided by restricting the dynamics of the
system to special decoherence-free subspaces. These subspaces are usually
constructed under the assumption of spatially symmetric system-bath coupling.
Here we show that decoherence-free subspaces may appear without spatial
symmetry. Instead, we consider a model of system-bath interactions in which to
first order only multiple-qubit coupling to the bath is present, with
single-qubit system-bath coupling absent. We derive necessary and sufficient
conditions for the appearance of decoherence-free states in this model, and
give a number of examples. In a sequel paper we show how to perform universal
and fault tolerant quantum computation on the decoherence-free subspaces
considered in this paper.Comment: 18 pages, no figures. Major changes. Section on universal fault
tolerant computation removed. This section contained a crucial error. A new
paper [quant-ph/0007013] presents the correct analysi
A Matrix model for plane partitions
We construct a matrix model equivalent (exactly, not asymptotically), to the
random plane partition model, with almost arbitrary boundary conditions.
Equivalently, it is also a random matrix model for a TASEP-like process with
arbitrary boundary conditions. Using the known solution of matrix models, this
method allows to find the large size asymptotic expansion of plane partitions,
to ALL orders. It also allows to describe several universal regimes.Comment: Latex, 41 figures. Misprints and corrections. Changing the term TASEP
to self avoiding particle porces