7,114 research outputs found
Improving zero-error classical communication with entanglement
Given one or more uses of a classical channel, only a certain number of
messages can be transmitted with zero probability of error. The study of this
number and its asymptotic behaviour constitutes the field of classical
zero-error information theory, the quantum generalisation of which has started
to develop recently. We show that, given a single use of certain classical
channels, entangled states of a system shared by the sender and receiver can be
used to increase the number of (classical) messages which can be sent with no
chance of error. In particular, we show how to construct such a channel based
on any proof of the Bell-Kochen-Specker theorem. This is a new example of the
use of quantum effects to improve the performance of a classical task. We
investigate the connection between this phenomenon and that of
``pseudo-telepathy'' games. The use of generalised non-signalling correlations
to assist in this task is also considered. In this case, a particularly elegant
theory results and, remarkably, it is sometimes possible to transmit
information with zero-error using a channel with no unassisted zero-error
capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus
figure 1 and the non-signalling box exampl
Multi-party zero-error classical channel coding with entanglement
We study the effects of quantum entanglement on the performance of two
classical zero-error communication tasks among multiple parties. Both tasks are
generalizations of the two-party zero-error channel-coding problem, where a
sender and a receiver want to perfectly communicate messages through a one-way
classical noisy channel. If the two parties are allowed to share entanglement,
there are several positive results that show the existence of channels for
which they can communicate strictly more than what they could do with classical
resources. In the first task, one sender wants to communicate a common message
to multiple receivers. We show that if the number of receivers is greater than
a certain threshold then entanglement does not allow for an improvement in the
communication for any finite number of uses of the channel. On the other hand,
when the number of receivers is fixed, we exhibit a class of channels for which
entanglement gives an advantage. The second problem we consider features
multiple collaborating senders and one receiver. Classically, cooperation among
the senders might allow them to communicate on average more messages than the
sum of their individual possibilities. We show that whenever a channel allows
single-sender entanglement-assisted advantage, then the gain extends also to
the multi-sender case. Furthermore, we show that entanglement allows for a
peculiar amplification of information which cannot happen classically, for a
fixed number of uses of a channel with multiple senders.Comment: Some proofs have been modifie
Entanglement-assisted zero-error source-channel coding
We study the use of quantum entanglement in the zero-error source-channel
coding problem. Here, Alice and Bob are connected by a noisy classical one-way
channel, and are given correlated inputs from a random source. Their goal is
for Bob to learn Alice's input while using the channel as little as possible.
In the zero-error regime, the optimal rates of source codes and channel codes
are given by graph parameters known as the Witsenhausen rate and Shannon
capacity, respectively. The Lov\'asz theta number, a graph parameter defined by
a semidefinite program, gives the best efficiently-computable upper bound on
the Shannon capacity and it also upper bounds its entanglement-assisted
counterpart. At the same time it was recently shown that the Shannon capacity
can be increased if Alice and Bob may use entanglement.
Here we partially extend these results to the source-coding problem and to
the more general source-channel coding problem. We prove a lower bound on the
rate of entanglement-assisted source-codes in terms Szegedy's number (a
strengthening of the theta number). This result implies that the theta number
lower bounds the entangled variant of the Witsenhausen rate. We also show that
entanglement can allow for an unbounded improvement of the asymptotic rate of
both classical source codes and classical source-channel codes. Our separation
results use low-degree polynomials due to Barrington, Beigel and Rudich,
Hadamard matrices due to Xia and Liu and a new application of remote state
preparation.Comment: Title has been changed. Previous title was 'Zero-error source-channel
coding with entanglement'. Corrected an error in Lemma 1.
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
We prove new bounds on the quantum communication complexity of the
disjointness and equality problems. For the case of exact and non-deterministic
protocols we show that these complexities are all equal to n+1, the previous
best lower bound being n/2. We show this by improving a general bound for
non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^*
n})-qubit bounded-error protocol for disjointness, modifying and improving the
earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an
Omega(sqrt{n}) lower bound for a large class of protocols that includes the
BCW-protocol as well as our new protocol.Comment: 11 pages LaTe
Quantum information and physics: Some future directions
I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity
A Generalization of Kochen-Specker Sets Relates Quantum Coloring to Entanglement-Assisted Channel Capacity
We introduce two generalizations of Kochen-Specker (KS) sets: projective KS
sets and generalized KS sets. We then use projective KS sets to characterize
all graphs for which the chromatic number is strictly larger than the quantum
chromatic number. Here, the quantum chromatic number is defined via a nonlocal
game based on graph coloring. We further show that from any graph with
separation between these two quantities, one can construct a classical channel
for which entanglement assistance increases the one-shot zero-error capacity.
As an example, we exhibit a new family of classical channels with an
exponential increase.Comment: 16 page
Entanglement can increase asymptotic rates of zero-error classical communication over classical channels
It is known that the number of different classical messages which can be
communicated with a single use of a classical channel with zero probability of
decoding error can sometimes be increased by using entanglement shared between
sender and receiver. It has been an open question to determine whether
entanglement can ever increase the zero-error communication rates achievable in
the limit of many channel uses. In this paper we show, by explicit examples,
that entanglement can indeed increase asymptotic zero-error capacity, even to
the extent that it is equal to the normal capacity of the channel.
Interestingly, our examples are based on the exceptional simple root systems E7
and E8.Comment: 14 pages, 2 figur
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