7,443 research outputs found
A most compendious and facile quantum de Finetti theorem
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's “exponential” approximation by “almost-product” states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choice of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems
Counterfactual Computation
Suppose that we are given a quantum computer programmed ready to perform a
computation if it is switched on. Counterfactual computation is a process by
which the result of the computation may be learnt without actually running the
computer. Such processes are possible within quantum physics and to achieve
this effect, a computer embodying the possibility of running the computation
must be available, even though the computation is, in fact, not run. We study
the possibilities and limitations of general protocols for the counterfactual
computation of decision problems (where the result r is either 0 or 1). If p(r)
denotes the probability of learning the result r ``for free'' in a protocol
then one might hope to design a protocol which simultaneously has large p(0)
and p(1). However we prove that p(0)+p(1) never exceeds 1 in any protocol and
we derive further constraints on p(0) and p(1) in terms of N, the number of
times that the computer is not run. In particular we show that any protocol
with p(0)+p(1)=1-epsilon must have N tending to infinity as epsilon tends to 0.
These general results are illustrated with some explicit protocols for
counterfactual computation. We show that "interaction-free" measurements can be
regarded as counterfactual computations, and our results then imply that N must
be large if the probability of interaction is to be close to zero. Finally, we
consider some ways in which our formulation of counterfactual computation can
be generalised.Comment: 19 pages. LaTex, 2 figures. Revised version has some new sections and
expanded explanation
Physical implementations of quantum absorption refrigerators
Absorption refrigerators are autonomous thermal machines that harness the
spontaneous flow of heat from a hot bath into the environment in order to
perform cooling. Here we discuss quantum realizations of absorption
refrigerators in two different settings: namely, cavity and circuit quantum
electrodynamics. We first provide a unified description of these machines in
terms of the concept of virtual temperature. Next, we describe the two
different physical setups in detail and compare their properties and
performance. We conclude with an outlook on future work and open questions in
this field of research.Comment: Patrick P. Potts was formerly known as Patrick P. Hofe
Novel steady state of a microtubule assembly in a confined geometry
We study the steady state of an assembly of microtubules in a confined
volume, analogous to the situation inside a cell where the cell boundary forms
a natural barrier to growth. We show that the dynamical equations for growing
and shrinking microtubules predict the existence of two steady states, with
either exponentially decaying or exponentially increasing distribution of
microtubule lengths. We identify the regimes in parameter space corresponding
to these steady states. In the latter case, the apparent catastrophe frequency
near the boundary was found to be significantly larger than that in the
interior. Both the exponential distribution of lengths and the increase in the
catastrophe frequency near the cell margin is in excellent agreement with
recent experimental observations.Comment: 8 pages, submitted to Phys. Rev.
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