11,599 research outputs found
Probabilistic Super Dense Coding
We explore the possibility of performing super dense coding with
non-maximally entangled states as a resource. Using this we find that one can
send two classical bits in a probabilistic manner by sending a qubit. We
generalize our scheme to higher dimensions and show that one can communicate
2log_2 d classical bits by sending a d-dimensional quantum state with a certain
probability of success. The success probability in super dense coding is
related to the success probability of distinguishing non-orthogonal states. The
optimal average success probabilities are explicitly calculated. We consider
the possibility of sending 2 log_2 d classical bits with a shared resource of a
higher dimensional entangled state (D X D, D > d). It is found that more
entanglement does not necessarily lead to higher success probability. This also
answers the question as to why we need log_2 d ebits to send 2 log_2 d
classical bits in a deterministic fashion.Comment: Latex file, no figures, 11 pages, Discussion changed in Section
Optimal dense coding with arbitrary pure entangled states
We examine dense coding with an arbitrary pure entangled state sharing
between the sender and the receiver. Upper bounds on the average success
probability in approximate dense coding and on the probability of conclusive
results in unambiguous dense coding are derived. We also construct the optimal
protocol which saturates the upper bound in each case.Comment: 5 pages, journal versio
Deterministic and Unambiguous Dense Coding
Optimal dense coding using a partially-entangled pure state of Schmidt rank
and a noiseless quantum channel of dimension is studied both in
the deterministic case where at most messages can be transmitted with
perfect fidelity, and in the unambiguous case where when the protocol succeeds
(probability ) Bob knows for sure that Alice sent message , and when
it fails (probability ) he knows it has failed. Alice is allowed any
single-shot (one use) encoding procedure, and Bob any single-shot measurement.
For a bound is obtained for in terms of the largest
Schmidt coefficient of the entangled state, and is compared with published
results by Mozes et al. For it is shown that is strictly
less than unless is an integer multiple of , in which case
uniform (maximal) entanglement is not needed to achieve the optimal protocol.
The unambiguous case is studied for , assuming for a
set of messages, and a bound is obtained for the average
\lgl1/\tau\rgl. A bound on the average \lgl\tau\rgl requires an additional
assumption of encoding by isometries (unitaries when ) that are
orthogonal for different messages. Both bounds are saturated when is a
constant independent of , by a protocol based on one-shot entanglement
concentration. For it is shown that (at least) messages can
be sent unambiguously. Whether unitary (isometric) encoding suffices for
optimal protocols remains a major unanswered question, both for our work and
for previous studies of dense coding using partially-entangled states,
including noisy (mixed) states.Comment: Short new section VII added. Latex 23 pages, 1 PSTricks figure in
tex
Genuine Multiparty Quantum Entanglement Suppresses Multiport Classical Information Transmission
We establish a universal complementarity relation between the capacity of
classical information transmission by employing a multiparty quantum state as a
multiport quantum channel, and the genuine multipartite entanglement of the
quantum state. The classical information transfer is from a sender to several
receivers by using the quantum dense coding protocol with the multiparty
quantum state shared between the sender and the receivers. The relation holds
for arbitrary pure or mixed quantum states of an arbitrary number of parties in
arbitrary dimensions.Comment: 5 (+ epsilon) pages, 2 figures, Revtex4-1; v2: Theorem 3 extended to
all states, other results unchange
- …