26 research outputs found
Transfer of quantum states using finite resources
We discuss the problem of transfering a qubit from Alice to Bob using a noisy
quantum channel and only finite resources. As the basic protocol for the
transfer we apply quantum teleportation. It turns out that for a certain
quality of the channel direct teleportation combined with qubit purification is
superior to entanglement purification of the channel. If, however, the quality
of the channel is rather low one should simply apply an estimation-preparation
scheme.Comment: 9 pages RevTeX including 5 figures, replaced with revised version, to
appear in Phys. Rev.
Collective versus local measurements on two parallel or antiparallel spins
We give a complete analysis of covariant measurements on two spins. We
consider the cases of two parallel and two antiparallel spins, and we consider
both collective measurements on the two spins, and measurements which require
only Local Quantum Operations and Classical Communication (LOCC). In all cases
we obtain the optimal measurements for arbitrary fidelities. In particular we
show that if the aim is determine as well as possible the direction in which
the spins are pointing, it is best to carry out measurements on antiparallel
spins (as already shown by Gisin and Popescu), second best to carry out
measurements on parallel spins and worst to be restricted to LOCC measurements.
If the the aim is to determine as well as possible a direction orthogonal to
that in which the spins are pointing, it is best to carry out measurements on
parallel spins, whereas measurements on antiparallel spins and LOCC
measurements are both less good but equivalent.Comment: 4 pages; minor revision
Optimal estimation of quantum dynamics
We construct the optimal strategy for the estimation of an unknown unitary
transformation . This includes, in addition to a convenient
measurement on a probe system, finding which is the best initial state on which
is to act. When , such an optimal strategy can be applied to
estimate simultaneously both the direction and the strength of a magnetic
field, and shows how to use a spin 1/2 particle to transmit information about a
whole coordinate system instead of only a direction in space.Comment: 4 pages, REVTE
Block Spin Density Matrix of the Inhomogeneous AKLT Model
We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain
model. Spins at each lattice site could be different. Under certain conditions,
the ground state of this AKLT model is unique and is described by the
Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous
block of bulk spins in this ground state. The density matrix is independent of
spins outside the block. It is diagonalized and shown to be a projector onto a
subspace. We prove that for large block the density matrix behaves as the
identity in the subspace. The von Neumann entropy coincides with Renyi entropy
and is equal to the saturated value.Comment: 20 page
Entanglement and Density Matrix of a Block of Spins in AKLT Model
We study a 1-dimensional AKLT spin chain, consisting of spins in the bulk
and at both ends. The unique ground state of this AKLT model is described
by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a
contiguous block of bulk spins in this ground state. It is shown that the
density matrix is a projector onto a subspace of dimension . This
subspace is described by non-zero eigenvalues and corresponding eigenvectors of
the density matrix. We prove that for large block the von Neumann entropy
coincides with Renyi entropy and is equal to .Comment: Revised version, typos corrected, references added, 31 page
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde