20 research outputs found
Unspeakable quantum information
No verbal explanation can indicate a direction in space or the orientation of
a coordinate system. Only material objects can do it. In this article we
consider the use of a set of spin-\half particles in an entangled state for
indicating a direction, or a hydrogen atom in a Rydberg state for transmitting
a Cartesian frame. Optimal strategies are derived for the emission and
detection of the quantum signals.Comment: to appear in "Quantum Theory: Reconsideration of Foundations", ed. by
A. Khrennikov; series ``Math. Modelling in Physics, Engineering and Cognitive
Sciences'' V\"axj\"o Univ. Press (2002) - requires sprocl.st
Weak limits for quantum random walks
We formulate and prove a general weak limit theorem for quantum random walks
in one and more dimensions. With denoting position at time , we show
that converges weakly as to a certain distribution which
is absolutely continuous and of bounded support. The proof is rigorous and
makes use of Fourier transform methods. This approach simplifies and extends
certain preceding derivations valid in one dimension that make use of
combinatorial and path integral methods
Covariant quantum measurements may not be optimal
Quantum particles, such as spins, can be used for communicating spatial
directions to observers who share no common coordinate frame. We show that if
the emitter's signals are the orbit of a group, then the optimal detection
method may not be a covariant measurement (contrary to widespread belief). It
may be advantageous for the receiver to use a different group and an indirect
estimation method: first, an ordinary measurement supplies redundant numerical
parameters; the latter are then used for a nonlinear optimal identification of
the signal.Comment: minor corrections, to appear in J. Mod. Opt. (proc. of Gdansk conf.
A de Finetti Representation Theorem for Quantum Process Tomography
In quantum process tomography, it is possible to express the experimenter's
prior information as a sequence of quantum operations, i.e., trace-preserving
completely positive maps. In analogy to de Finetti's concept of exchangeability
for probability distributions, we give a definition of exchangeability for
sequences of quantum operations. We then state and prove a representation
theorem for such exchangeable sequences. The theorem leads to a simple
characterization of admissible priors for quantum process tomography and solves
to a Bayesian's satisfaction the problem of an unknown quantum operation.Comment: 10 page
Bounded Entanglement Entropy in the Quantum Ising Model
Funder: University of CambridgeAbstract: A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of the stochastic geometric arguments in the earlier work by Grimmett et al. (J Stat Phys 131:305–339, 2008). The proof utilises a transformation to a model of classical probability called the continuum random-cluster model. Our method of proof is fairly robust, and applies also to certain disordered systems
Entanglement in the quantum Ising model
We study the asymptotic scaling of the entanglement of a block of spins for
the ground state of the one-dimensional quantum Ising model with transverse
field. When the field is sufficiently strong, the entanglement grows at most
logarithmically in the number of spins. The proof utilises a transformation to
a model of classical probability called the continuum random-cluster model, and
is based on a property of the latter model termed ratio weak-mixing. Our proof
applies equally to a large class of disordered interactions