73 research outputs found
An improved rate region for the classical-quantum broadcast channel
We present a new achievable rate region for the two-user binary-input
classical-quantum broadcast channel. The result is a generalization of the
classical Marton-Gelfand-Pinsker region and is provably larger than the best
previously known rate region for classical-quantum broadcast channels. The
proof of achievability is based on the recently introduced polar coding scheme
and its generalization to quantum network information theory.Comment: 5 pages, double column, 1 figure, based on a result presented in the
Master's thesis arXiv:1501.0373
The strong converse theorem for the product-state capacity of quantum channels with ergodic Markovian memory
Establishing the strong converse theorem for a communication channel confirms
that the capacity of that channel, that is, the maximum achievable rate of
reliable information communication, is the ultimate limit of communication over
that channel. Indeed, the strong converse theorem for a channel states that
coding at a rate above the capacity of the channel results in the convergence
of the error to its maximum value 1 and that there is no trade-off between
communication rate and decoding error. Here we prove that the strong converse
theorem holds for the product-state capacity of quantum channels with ergodic
Markovian correlated memory.Comment: 11 pages, single colum
Efficient achievability for quantum protocols using decoupling theorems
Proving achievability of protocols in quantum Shannon theory usually does not
consider the efficiency at which the goal of the protocol can be achieved.
Nevertheless it is known that protocols such as coherent state merging are
efficiently achievable at optimal rate. We aim to investigate this fact further
in a general one-shot setting, by considering certain classes of decoupling
theorems and give exact rates for these classes. Moreover we compare results of
general decoupling theorems using Haar distributed unitaries with those using
smaller sets of operators, in particular -approximate 2-designs. We
also observe the behavior of our rates in special cases such as
approaching zero and the asymptotic limit.Comment: 5 pages, double column, v2: added referenc
Polar codes in network quantum information theory
Polar coding is a method for communication over noisy classical channels
which is provably capacity-achieving and has an efficient encoding and
decoding. Recently, this method has been generalized to the realm of quantum
information processing, for tasks such as classical communication, private
classical communication, and quantum communication. In the present work, we
apply the polar coding method to network quantum information theory, by making
use of recent advances for related classical tasks. In particular, we consider
problems such as the compound multiple access channel and the quantum
interference channel. The main result of our work is that it is possible to
achieve the best known inner bounds on the achievable rate regions for these
tasks, without requiring a so-called quantum simultaneous decoder. Thus, our
work paves the way for developing network quantum information theory further
without requiring a quantum simultaneous decoder.Comment: 18 pages, 2 figures, v2: 10 pages, double column, version accepted
for publicatio
Decoupling with random diagonal unitaries
We investigate decoupling, one of the most important primitives in quantum
Shannon theory, by replacing the uniformly distributed random unitaries
commonly used to achieve the protocol, with repeated applications of random
unitaries diagonal in the Pauli- and - bases. This strategy was recently
shown to achieve an approximate unitary -design after a number of
repetitions of the process, which implies that the strategy gradually achieves
decoupling. Here, we prove that even fewer repetitions of the process achieve
decoupling at the same rate as that with the uniform ones, showing that rather
imprecise approximations of unitary -designs are sufficient for decoupling.
We also briefly discuss efficient implementations of them and implications of
our decoupling theorem to coherent state merging and relative thermalisation.Comment: 26 pages, 3 figures. v2: 19 pages, 3 figures, both results and
presentations are improved. One conjecture in the previous version was
proven. v3: 16 pages, 1 figure. v4: doi links are added, published versio
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
Calculating a maximizer for Quantum mutual information
We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels
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