1,917 research outputs found

### Distilling common randomness from bipartite quantum states

The problem of converting noisy quantum correlations between two parties into
noiseless classical ones using a limited amount of one-way classical
communication is addressed. A single-letter formula for the optimal trade-off
between the extracted common randomness and classical communication rate is
obtained for the special case of classical-quantum correlations. The resulting
curve is intimately related to the quantum compression with classical side
information trade-off curve $Q^*(R)$ of Hayden, Jozsa and Winter. For a general
initial state we obtain a similar result, with a single-letter formula, when we
impose a tensor product restriction on the measurements performed by the
sender; without this restriction the trade-off is given by the regularization
of this function. Of particular interest is a quantity we call ``distillable
common randomness'' of a state: the maximum overhead of the common randomness
over the one-way classical communication if the latter is unbounded. It is an
operational measure of (total) correlation in a quantum state. For
classical-quantum correlations it is given by the Holevo mutual information of
its associated ensemble, for pure states it is the entropy of entanglement. In
general, it is given by an optimization problem over measurements and
regularization; for the case of separable states we show that this can be
single-letterized.Comment: 22 pages, LaTe

### Relating quantum privacy and quantum coherence: an operational approach

We describe how to achieve optimal entanglement generation and one-way
entanglement distillation rates by coherent implementation of a class of secret
key generation and secret key distillation protocols, respectively.
This short paper is a high-level descrioption of our detailed papers [8] and
[10].Comment: 4 pages, revtex

### A Resource Framework for Quantum Shannon Theory

Quantum Shannon theory is loosely defined as a collection of coding theorems,
such as classical and quantum source compression, noisy channel coding
theorems, entanglement distillation, etc., which characterize asymptotic
properties of quantum and classical channels and states. In this paper we
advocate a unified approach to an important class of problems in quantum
Shannon theory, consisting of those that are bipartite, unidirectional and
memoryless.
We formalize two principles that have long been tacitly understood. First, we
describe how the Church of the larger Hilbert space allows us to move flexibly
between states, channels, ensembles and their purifications. Second, we
introduce finite and asymptotic (quantum) information processing resources as
the basic objects of quantum Shannon theory and recast the protocols used in
direct coding theorems as inequalities between resources. We develop the rules
of a resource calculus which allows us to manipulate and combine resource
inequalities. This framework simplifies many coding theorem proofs and provides
structural insights into the logical dependencies among coding theorems.
We review the above-mentioned basic coding results and show how a subset of
them can be unified into a family of related resource inequalities. Finally, we
use this family to find optimal trade-off curves for all protocols involving
one noisy quantum resource and two noiseless ones.Comment: 60 page

### A family of quantum protocols

We introduce two dual, purely quantum protocols: for entanglement
distillation assisted by quantum communication (``mother'' protocol) and for
entanglement assisted quantum communication (``father'' protocol). We show how
a large class of ``children'' protocols (including many previously known ones)
can be derived from the two by direct application of teleportation or
super-dense coding. Furthermore, the parent may be recovered from most of the
children protocols by making them ``coherent''. We also summarize the various
resource trade-offs these protocols give rise to.Comment: 5 pages, 1 figur

### 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

### Distillation of local purity from quantum states

Recently Horodecki et al. [Phys. Rev. Lett. 90, 100402 (2003)] introduced an
important quantum information processing paradigm, in which two parties sharing
many copies of the same bipartite quantum state distill local pure states, by
means of local unitary operations assisted by a one-way (two-way) completely
dephasing channel. Local pure states are a valuable resource from a
thermodynamical point of view, since they allow thermal energy to be converted
into work by local quantum heat engines. We give a simple
information-theoretical characterization of the one-way distillable local
purity, which turns out to be closely related to a previously known operational
measure of classical correlations, the one-way distillable common randomness.Comment: 8 page

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