667 research outputs found
Distillation of secret key and entanglement from quantum states
We study and solve the problem of distilling secret key from quantum states
representing correlation between two parties (Alice and Bob) and an
eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to
achieve the "wire-tapper" bound, the difference of the mutual information
Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way
public communication.
This result yields information--theoretic formulas for the distillable secret
key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a
purification of Alice and Bob's joint state.
Specialising our protocol somewhat and making it coherent leads us to a
protocol of entanglement distillation via one-way LOCC (local operations and
classical communication) which is asymptotically optimal: in fact we prove the
so-called "hashing inequality" which says that the coherent information (i.e.,
the negative conditional von Neumann entropy) is an achievable EPR rate.
This result is well--known to imply a whole set of distillation and capacity
formulas which we briefly review.Comment: 17 pages LaTeX, 1 drawing (eps
Exact Cost of Redistributing Multipartite Quantum States
How correlated are two quantum systems from the perspective of a third? We answer this by providing an optimal “quantum state redistribution” protocol for multipartite product sources. Specifically, given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, we identify the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob. The communication cost gives the first known operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived
Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
We consider quantum channels with two senders and one receiver. For an
arbitrary such channel, we give multi-letter characterizations of two different
two-dimensional capacity regions. The first region is comprised of the rates at
which it is possible for one sender to send classical information, while the
other sends quantum information. The second region consists of the rates at
which each sender can send quantum information. For each region, we give an
example of a channel for which the corresponding region has a single-letter
description. One of our examples relies on a new result proved here, perhaps of
independent interest, stating that the coherent information over any degradable
channel is concave in the input density operator. We conclude with connections
to other work and a discussion on generalizations where each user
simultaneously sends classical and quantum information.Comment: 38 pages, 1 figure. Fixed typos, added new example. Submitted to IEEE
Tranactions on Information Theor
Quantum broadcast channels
We consider quantum channels with one sender and two receivers, used in
several different ways for the simultaneous transmission of independent
messages. We begin by extending the technique of superposition coding to
quantum channels with a classical input to give a general achievable region. We
also give outer bounds to the capacity regions for various special cases from
the classical literature and prove that superposition coding is optimal for a
class of channels. We then consider extensions of superposition coding for
channels with a quantum input, where some of the messages transmitted are
quantum instead of classical, in the sense that the parties establish bipartite
or tripartite GHZ entanglement. We conclude by using state merging to give
achievable rates for establishing bipartite entanglement between different
pairs of parties with the assistance of free classical communication.Comment: 15 pages; IEEE Trans. Inform. Theory, vol. 57, no. 10, October 201
Bounds on classical information capacities for a class of quantum memory channels
The maximum rates for information transmission through noisy quantum channels
has primarily been developed for memoryless channels, where the noise on each
transmitted state is treated as independent. Many real world communication
channels experience noise which is modelled better by errors that are
correlated between separate channel uses. In this paper, upper bounds on the
classical information capacities of a class of quantum memory channels are
derived. The class of channels consists of indecomposable quantum memory
channels, a generalization of classical indecomposable finite-state channels.Comment: 4 pages, 1 figure, RevTeX, coding theorem remove
Capacity Theorems for Quantum Multiple Access Channels
We consider quantum channels with two senders and one receiver. For an
arbitrary such channel, we give multi-letter characterizations of two different
two-dimensional capacity regions. The first region characterizes the rates at
which it is possible for one sender to send classical information while the
other sends quantum information. The second region gives the rates at which
each sender can send quantum information. We give an example of a channel for
which each region has a single-letter description, concluding with a
characterization of the rates at which each user can simultaneously send
classical and quantum information.Comment: 5 pages. Conference version of quant-ph/0501045, to appear in the
proceedings of the IEEE International Symposium on Information Theory,
Adelaide, Australia, 200
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