341 research outputs found
Quantum Channel Capacities Per Unit Cost
Communication over a noisy channel is often conducted in a setting in which
different input symbols to the channel incur a certain cost. For example, for
bosonic quantum channels, the cost associated with an input state is the number
of photons, which is proportional to the energy consumed. In such a setting, it
is often useful to know the maximum amount of information that can be reliably
transmitted per cost incurred. This is known as the capacity per unit cost. In
this paper, we generalize the capacity per unit cost to various communication
tasks involving a quantum channel such as classical communication,
entanglement-assisted classical communication, private communication, and
quantum communication. For each task, we define the corresponding capacity per
unit cost and derive a formula for it analogous to that of the usual capacity.
Furthermore, for the special and natural case in which there is a zero-cost
state, we obtain expressions in terms of an optimized relative entropy
involving the zero-cost state. For each communication task, we construct an
explicit pulse-position-modulation coding scheme that achieves the capacity per
unit cost. Finally, we compute capacities per unit cost for various bosonic
Gaussian channels and introduce the notion of a blocklength constraint as a
proposed solution to the long-standing issue of infinite capacities per unit
cost. This motivates the idea of a blocklength-cost duality, on which we
elaborate in depth.Comment: v3: 18 pages, 2 figure
Experimental detection of quantum channel capacities
We present an effcient experimental procedure that certifies non vanishing
quantum capacities for qubit noisy channels. Our method is based on the use of
a fixed bipartite entangled state, where the system qubit is sent to the
channel input. A particular set of local measurements is performed at the
channel output and the ancilla qubit mode, obtaining lower bounds to the
quantum capacities for any unknown channel with no need of a quantum process
tomography. The entangled qubits have a Bell state configuration and are
encoded in photon polarization. The lower bounds are found by estimating the
Shannon and von Neumann entropies at the output using an optimized basis, whose
statistics is obtained by measuring only the three observables
, and
.Comment: 5 pages and 3 figures in the principal article, and 4 pages in the
supplementary materia
Efficient Approximation of Quantum Channel Capacities
We propose an iterative method for approximating the capacity of
classical-quantum channels with a discrete input alphabet and a finite
dimensional output, possibly under additional constraints on the input
distribution. Based on duality of convex programming, we derive explicit upper
and lower bounds for the capacity. To provide an -close estimate
to the capacity, the presented algorithm requires , where denotes the input alphabet size and
the output dimension. We then generalize the method for the task of
approximating the capacity of classical-quantum channels with a bounded
continuous input alphabet and a finite dimensional output. For channels with a
finite dimensional quantum mechanical input and output, the idea of a universal
encoder allows us to approximate the Holevo capacity using the same method. In
particular, we show that the problem of approximating the Holevo capacity can
be reduced to a multidimensional integration problem. For families of quantum
channels fulfilling a certain assumption we show that the complexity to derive
an -close solution to the Holevo capacity is subexponential or
even polynomial in the problem size. We provide several examples to illustrate
the performance of the approximation scheme in practice.Comment: 36 pages, 1 figur
Quantum Channel Capacities with Passive Environment Assistance
We initiate the study of passive environment-assisted communication via a
quantum channel, modeled as a unitary interaction between the information
carrying system and an environment. In this model, the environment is
controlled by a benevolent helper who can set its initial state such as to
assist sender and receiver of the communication link. (The case of a malicious
environment, also known as jammer, or arbitrarily varying channel, is
essentially well-understood and comprehensively reviewed.) Here, after setting
out precise definitions, focussing on the problem of quantum communication, we
show that entanglement plays a crucial role in this problem: indeed, the
assisted capacity where the helper is restricted to product states between
channel uses is different from the one with unrestricted helper. Furthermore,
prior shared entanglement between the helper and the receiver makes a
difference, too.Comment: 14 pages, 13 figures, IEEE format, Theorem 9 (statement and proof)
changed, updated References and Example 11 added. Comments are welcome
Additivity of Entangled Channel Capacity for Quantum Input States
An elementary introduction into algebraic approach to unified quantum
information theory and operational approach to quantum entanglement as
generalized encoding is given. After introducing compound quantum state and two
types of informational divergences, namely, Araki-Umegaki (a-type) and of
Belavkin-Staszewski (b-type) quantum relative entropic information, this paper
treats two types of quantum mutual information via entanglement and defines two
types of corresponding quantum channel capacities as the supremum via the
generalized encodings. It proves the additivity property of quantum channel
capacities via entanglement, which extends the earlier results of V. P.
Belavkin to products of arbitrary quantum channels for quantum relative entropy
of any type.Comment: 17 pages. See the related papers at
http://www.maths.nott.ac.uk/personal/vpb/research/ent_com.htm
Continuity of quantum channel capacities
We prove that a broad array of capacities of a quantum channel are
continuous. That is, two channels that are close with respect to the diamond
norm have correspondingly similar communication capabilities. We first show
that the classical capacity, quantum capacity, and private classical capacity
are continuous, with the variation on arguments epsilon apart bounded by a
simple function of epsilon and the channel's output dimension. Our main tool is
an upper bound of the variation of output entropies of many copies of two
nearby channels given the same initial state; the bound is linear in the number
of copies. Our second proof is concerned with the quantum capacities in the
presence of free backward or two-way public classical communication. These
capacities are proved continuous on the interior of the set of non-zero
capacity channels by considering mutual simulation between similar channels.Comment: 12 pages, Revised according to referee's suggestion
A Survey on Quantum Channel Capacities
Quantum information processing exploits the quantum nature of information. It
offers fundamentally new solutions in the field of computer science and extends
the possibilities to a level that cannot be imagined in classical communication
systems. For quantum communication channels, many new capacity definitions were
developed in comparison to classical counterparts. A quantum channel can be
used to realize classical information transmission or to deliver quantum
information, such as quantum entanglement. Here we review the properties of the
quantum communication channel, the various capacity measures and the
fundamental differences between the classical and quantum channels.Comment: 58 pages, Journal-ref: IEEE Communications Surveys and Tutorials
(2018) (updated & improved version of arXiv:1208.1270
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