49 research outputs found
Entanglement-Assisted Capacity of Quantum Multiple-Access Channels
We find a regularized formula for the entanglement-assisted (EA) capacity
region for quantum multiple access channels (QMAC). We illustrate the capacity
region calculation with the example of the collective phase-flip channel which
admits a single-letter characterization. On the way, we provide a
first-principles proof of the EA coding theorem based on a packing argument. We
observe that the Holevo-Schumacher-Westmoreland theorem may be obtained from a
modification of our EA protocol. We remark on the existence of a family
hierarchy of protocols for multiparty scenarios with a single receiver, in
analogy to the two-party case. In this way, we relate several previous results
regarding QMACs.Comment: Published version. 13 pages, 3 figure
Superadditivity of the Classical Capacity with Limited Entanglement Assistance
Finding the optimal encoding strategies can be challenging for communication
using quantum channels, as classical and quantum capacities may be
superadditive. Entanglement assistance can often simplify this task, as the
entanglement-assisted classical capacity for any channel is additive, making
entanglement across channel uses unnecessary. If the entanglement assistance is
limited, the picture is much more unclear. Suppose the classical capacity is
superadditive, then the classical capacity with limited entanglement assistance
could retain superadditivity by continuity arguments. If the classical capacity
is additive, it is unknown if superadditivity can still be developed with
limited entanglement assistance. We show this is possible, by providing an
example. We construct a channel for which, the classical capacity is additive,
but that with limited entanglement assistance can be superadditive. This shows
entanglement plays a weird role in communication and we still understand very
little about it.Comment: 13 page
On the Second-Order Asymptotics for Entanglement-Assisted Communication
The entanglement-assisted classical capacity of a quantum channel is known to
provide the formal quantum generalization of Shannon's classical channel
capacity theorem, in the sense that it admits a single-letter characterization
in terms of the quantum mutual information and does not increase in the
presence of a noiseless quantum feedback channel from receiver to sender. In
this work, we investigate second-order asymptotics of the entanglement-assisted
classical communication task. That is, we consider how quickly the rates of
entanglement-assisted codes converge to the entanglement-assisted classical
capacity of a channel as a function of the number of channel uses and the error
tolerance. We define a quantum generalization of the mutual information
variance of a channel in the entanglement-assisted setting. For covariant
channels, we show that this quantity is equal to the channel dispersion, and
thus completely characterize the convergence towards the entanglement-assisted
classical capacity when the number of channel uses increases. Our results also
apply to entanglement-assisted quantum communication, due to the equivalence
between entanglement-assisted classical and quantum communication established
by the teleportation and super-dense coding protocols.Comment: v2: Accepted for publication in Quantum Information Processin
One-shot entanglement-assisted quantum and classical communication
We study entanglement-assisted quantum and classical communication over a
single use of a quantum channel, which itself can correspond to a finite number
of uses of a channel with arbitrarily correlated noise. We obtain
characterizations of the corresponding one-shot capacities by establishing
upper and lower bounds on them in terms of the difference of two smoothed
entropic quantities. In the case of a memoryless channel, the upper and lower
bounds converge to the known single-letter formulas for the corresponding
capacities, in the limit of asymptotically many uses of it. Our results imply
that the difference of two smoothed entropic quantities characterizing the
one-shot entanglement-assisted capacities serves as a one-shot analogue of the
mutual information, since it reduces to the mutual information, between the
output of the channel and a system purifying its input, in the asymptotic,
memoryless scenario.Comment: 10 pages, 2 figures. Title changed due to new results on the one-shot
entanglement-assisted quantum communication. In addition, an error in the
previous version regarding the converse proof of the one-shot EAC capacity
has been correcte
A father protocol for quantum broadcast channels
A new protocol for quantum broadcast channels based on the fully quantum
Slepian-Wolf protocol is presented. The protocol yields an achievable rate
region for entanglement-assisted transmission of quantum information through a
quantum broadcast channel that can be considered the quantum analogue of
Marton's region for classical broadcast channels. The protocol can be adapted
to yield achievable rate regions for unassisted quantum communication and for
entanglement-assisted classical communication; in the case of unassisted
transmission, the region we obtain has no independent constraint on the sum
rate, only on the individual transmission rates. Regularized versions of all
three rate regions are provably optimal.Comment: Typo in statement of Theorem 4 fixe
Secure Communication with Unreliable Entanglement Assistance
Secure communication is considered with unreliable entanglement assistance,
where the adversary may intercept the legitimate receiver's entanglement
resource before communication takes place. The communication setting of
unreliable assistance, without security aspects, was originally motivated by
the extreme photon loss in practical communication systems. The operational
principle is to adapt the transmission rate to the availability of entanglement
assistance, without resorting to feedback and repetition. Here, we require
secrecy as well. An achievable secrecy rate region is derived for general
quantum wiretap channels, and a multi-letter secrecy capacity formula for the
special class of degraded channels
Universal coding for transmission of private information
We consider the scenario in which Alice transmits private classical messages
to Bob via a classical-quantum channel, part of whose output is intercepted by
an eavesdropper, Eve. We prove the existence of a universal coding scheme under
which Alice's messages can be inferred correctly by Bob, and yet Eve learns
nothing about them. The code is universal in the sense that it does not depend
on specific knowledge of the channel. Prior knowledge of the probability
distribution on the input alphabet of the channel, and bounds on the
corresponding Holevo quantities of the output ensembles at Bob's and Eve's end
suffice.Comment: 31 pages, no figures. Published versio