702 research outputs found
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
Quantum Clock Synchronization: a Multi-Party Protocol
We present a multi-party quantum clock synchronization protocol that utilizes
shared prior entanglement and broadcast of classical information to synchronize
spatially separated clocks. Notably, it is necessary only for any one party to
publish classical information. Consequently, the efficacy of the method is
independent of the relative location of the parties. The suggested protocol is
robust and does not require precise sequencing of procedural steps.Comment: 3 page
Compatibility of quantum states
We introduce a measure of the compatibility between quantum states--the
likelihood that two density matrices describe the same object. Our measure is
motivated by two elementary requirements, which lead to a natural definition.
We list some properties of this measure, and discuss its relation to the
problem of combining two observers' states of knowledge.Comment: 4 pages, no figure
Quantum Algorithms: Entanglement Enhanced Information Processing
We discuss the fundamental role of entanglement as the essential nonclassical
feature providing the computational speed-up in the known quantum algorithms.
We review the construction of the Fourier transform on an Abelian group and the
principles underlying the fast Fourier transform algorithm. We describe the
implementation of the FFT algorithm for the group of integers modulo 2^n in the
quantum context, showing how the group-theoretic formalism leads to the
standard quantum network and identifying the property of entanglement that
gives rise to the exponential speedup (compared to the classical FFT). Finally
we outline the use of the Fourier transform in extracting periodicities, which
underlies its utility in the known quantum algorithms.Comment: 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc.
(Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum
Computation: Theory and Experiment'', held in November 199
A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
Two quantum information processing protocols are said to be dual under
resource reversal if the resources consumed (generated) in one protocol are
generated (consumed) in the other. Previously known examples include the
duality between entanglement concentration and dilution, and the duality
between coherent versions of teleportation and super-dense coding. A quantum
feedback channel is an isometry from a system belonging to Alice to a system
shared between Alice and Bob. We show that such a resource may be reversibly
decomposed into a perfect quantum channel and pure entanglement, generalizing
both of the above examples. The dual protocols responsible for this
decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum
reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf''
protocol (FQSW), a generalization of the recently discovered ``quantum state
merging'', is related to FF by source-channel duality, and to FQRS by time
reversal duality, thus forming a triangle of dualities. The source-channel
duality is identified as the origin of the previously poorly understood
``mother-father'' duality. Due to a symmetry breaking, the dualities extend
only partially to classical information theory.Comment: 5 pages, 5 figure
Towards a geometrical interpretation of quantum information compression
Let S be the von Neumann entropy of a finite ensemble E of pure quantum
states. We show that S may be naturally viewed as a function of a set of
geometrical volumes in Hilbert space defined by the states and that S is
monotonically increasing in each of these variables. Since S is the Schumacher
compression limit of E, this monotonicity property suggests a geometrical
interpretation of the quantum redundancy involved in the compression process.
It provides clarification of previous work in which it was shown that S may be
increased while increasing the overlap of each pair of states in the ensemble.
As a byproduct, our mathematical techniques also provide a new interpretation
of the subentropy of E.Comment: 11 pages, latex2
Entanglement cost of two-qubit orthogonal measurements
The "entanglement cost" of a bipartite measurement is the amount of shared
entanglement two participants need to use up in order to carry out the given
measurement by means of local operations and classical communication. Here we
numerically investigate the entanglement cost of generic orthogonal
measurements on two qubits. Our results strongly suggest that for almost all
measurements of this kind, the entanglement cost is strictly greater than the
average entanglement of the eigenstates associated with the measurements,
implying that the nonseparability of a two-qubit orthogonal measurement is
generically distinct from the nonseparability of its eigenstates.Comment: Latex, 4 pages, minor change
Universal Quantum Information Compression
Suppose that a quantum source is known to have von Neumann entropy less than
or equal to S but is otherwise completely unspecified. We describe a method of
universal quantum data compression which will faithfully compress the quantum
information of any such source to S qubits per signal (in the limit of large
block lengths).Comment: RevTex 4 page
Distinguishability of States and von Neumann Entropy
Consider an ensemble of pure quantum states |\psi_j>, j=1,...,n taken with
prior probabilities p_j respectively. We show that it is possible to increase
all of the pairwise overlaps || i.e. make each constituent pair
of the states more parallel (while keeping the prior probabilities the same),
in such a way that the von Neumann entropy S is increased, and dually, make all
pairs more orthogonal while decreasing S. We show that this phenomenon cannot
occur for ensembles in two dimensions but that it is a feature of almost all
ensembles of three states in three dimensions. It is known that the von Neumann
entropy characterises the classical and quantum information capacities of the
ensemble and we argue that information capacity in turn, is a manifestation of
the distinguishability of the signal states. Hence our result shows that the
notion of distinguishability within an ensemble is a global property that
cannot be reduced to considering distinguishability of each constituent pair of
states.Comment: 18 pages, Latex, 2 figure
- …