2,027 research outputs found
Quantum Entanglement Capacity with Classical Feedback
For any quantum discrete memoryless channel, we define a quantity called
quantum entanglement capacity with classical feedback (), and we show that
this quantity lies between two other well-studied quantities. These two
quantities - namely the quantum capacity assisted by two-way classical
communication () and the quantum capacity with classical feedback ()
- are widely conjectured to be different: there exists quantum discrete
memoryless channel for which . We then present a general scheme to
convert any quantum error-correcting codes into adaptive protocols for this
newly-defined quantity of the quantum depolarizing channel, and illustrate with
Cat (repetition) code and Shor code. We contrast the present notion with
entanglement purification protocols by showing that whilst the Leung-Shor
protocol can be applied directly, recurrence methods need to be supplemented
with other techniques but at the same time offer a way to improve the
aforementioned Cat code. For the quantum depolarizing channel, we prove a
formula that gives lower bounds on the quantum capacity with classical feedback
from any protocols. We then apply this formula to the protocols
that we discuss to obtain new lower bounds on the quantum capacity with
classical feedback of the quantum depolarizing channel
On the complementary quantum capacity of the depolarizing channel
The qubit depolarizing channel with noise parameter transmits an input
qubit perfectly with probability , and outputs the completely mixed
state with probability . We show that its complementary channel has
positive quantum capacity for all . Thus, we find that there exists a
single parameter family of channels having the peculiar property of having
positive quantum capacity even when the outputs of these channels approach a
fixed state independent of the input. Comparisons with other related channels,
and implications on the difficulty of studying the quantum capacity of the
depolarizing channel are discussed.Comment: v4 corrects errors in equation (38
Quantum and private capacities of low-noise channels
We determine both the quantum and the private capacities of low-noise quantum
channels to leading orders in the channel's distance to the perfect channel. It
has been an open problem for more than 20 years to determine the capacities of
some of these low-noise channels such as the depolarizing channel. We also show
that both capacities are equal to the single-letter coherent information of the
channel, again to leading orders. We thus find that, in the low noise regime,
super-additivity and degenerate codes have negligible benefit for the quantum
capacity, and shielding does not improve the private capacity beyond the
quantum capacity, in stark contrast to the situation when noisier channels are
considered.Comment: 23 pages, 4 figures, comments welcome! v2: improved bounds on
degradability parameters and capacities of depolarizing channel and XZ
channel (see also ancillary files 'depol-deg-bound.nb' and
'XZ-deg-bound.nb'), extension of results to generalized low-noise channels.
v3: strengthened version of Lemma
The classical capacity of quantum channels with memory
We investigate the classical capacity of two quantum channels with memory: a
periodic channel with depolarizing channel branches, and a convex combination
of depolarizing channels. We prove that the capacity is additive in both cases.
As a result, the channel capacity is achieved without the use of entangled
input states. In the case of a convex combination of depolarizing channels the
proof provided can be extended to other quantum channels whose classical
capacity has been proved to be additive in the memoryless case.Comment: 6 double-column pages. Short note added on quantum memory channel
Quantum cloning and the capacity of the Pauli channel
A family of quantum cloning machines is introduced that produce two
approximate copies from a single quantum bit, while the overall input-to-output
operation for each copy is a Pauli channel. A no-cloning inequality is derived,
describing the balance between the quality of the two copies. This also
provides an upper bound on the quantum capacity of the Pauli channel with
probabilities , and . The capacity is shown to be vanishing if
lies outside an ellipsoid whose pole
coincides with the depolarizing channel that underlies the universal cloning
machine.Comment: 5 pages RevTeX, 3 Postscript figure
The quantum capacity with symmetric side channels
We present an upper bound for the quantum channel capacity that is both
additive and convex. Our bound can be interpreted as the capacity of a channel
for high-fidelity quantum communication when assisted by a family of channels
that have no capacity on their own. This family of assistance channels, which
we call symmetric side channels, consists of all channels mapping symmetrically
to their output and environment. The bound seems to be quite tight, and for
degradable quantum channels it coincides with the unassisted channel capacity.
Using this symmetric side channel capacity, we find new upper bounds on the
capacity of the depolarizing channel. We also briefly indicate an analogous
notion for distilling entanglement using the same class of (one-way) channels,
yielding one of the few entanglement measures that is monotonic under local
operations with one-way classical communication (1-LOCC), but not under the
more general class of local operations with classical communication (LOCC).Comment: 10 pages, 4 figure
Classical capacity of a qubit depolarizing channel with memory
The classical product state capacity of a noisy quantum channel with memory
is investigated. A forgetful noise-memory channel is constructed by Markov
switching between two depolarizing channels which introduces non-Markovian
noise correlations between successive channel uses. The computation of the
capacity is reduced to an entropy computation for a function of a Markov
process. A reformulation in terms of algebraic measures then enables its
calculation. The effects of the hidden-Markovian memory on the capacity are
explored. An increase in noise-correlations is found to increase the capacity
On the von Neumann capacity of noisy quantum channels
We discuss the capacity of quantum channels for information transmission and
storage. Quantum channels have dual uses: they can be used to transmit known
quantum states which code for classical information, and they can be used in a
purely quantum manner, for transmitting or storing quantum entanglement. We
propose here a definition of the von Neumann capacity of quantum channels,
which is a quantum mechanical extension of the Shannon capacity and reverts to
it in the classical limit. As such, the von Neumann capacity assumes the role
of a classical or quantum capacity depending on the usage of the channel. In
analogy to the classical construction, this capacity is defined as the maximum
von Neumann mutual entropy processed by the channel, a measure which reduces to
the capacity for classical information transmission through quantum channels
(the "Kholevo capacity") when known quantum states are sent. The quantum mutual
entropy fulfills all basic requirements for a measure of information, and
observes quantum data-processing inequalities. We also derive a quantum Fano
inequality relating the quantum loss of the channel to the fidelity of the
quantum code. The quantities introduced are calculated explicitly for the
quantum "depolarizing" channel. The von Neumann capacity is interpreted within
the context of superdense coding, and an "extended" Hamming bound is derived
that is consistent with that capacity.Comment: 15 pages RevTeX with psfig, 13 figures. Revised interpretation of
capacity, added section, changed titl
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