26,263 research outputs found
Entanglement required in achieving entanglement-assisted channel capacities
Entanglement shared between the two ends of a quantum communication channel
has been shown to be a useful resource in increasing both the quantum and
classical capacities for these channels. The entanglement-assisted capacities
were derived assuming an unlimited amount of shared entanglement per channel
use. In this paper, bounds are derived on the minimum amount of entanglement
required per use of a channel, in order to asymptotically achieve the capacity.
This is achieved by introducing a class of entanglement-assisted quantum codes.
Codes for classes of qubit channels are shown to achieve the quantum
entanglement-assisted channel capacity when an amount of shared entanglement
per channel given by, E = 1 - Q_E, is provided. It is also shown that for very
noisy channels, as the capacities become small, the amount of required
entanglement converges for the classical and quantum capacities.Comment: 9 pages, 2 figures, RevTex
Quantum Feedback Channels
In Shannon information theory the capacity of a memoryless communication
channel cannot be increased by the use of feedback. In quantum information
theory the no-cloning theorem means that noiseless copying and feedback of
quantum information cannot be achieved. In this paper, quantum feedback is
defined as the unlimited use of a noiseless quantum channel from receiver to
sender. Given such quantum feedback, it is shown to provide no increase in the
entanglement--assisted capacities of a memoryless quantum channel, in direct
analogy to the classical case. It is also shown that in various cases of
non-assisted capacities, feedback may increase the capacity of memoryless
quantum channels.Comment: 5 pages, requires IEEEtran.cls, expanded, proofs added, references
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Additive Extensions of a Quantum Channel
We study extensions of a quantum channel whose one-way capacities are
described by a single-letter formula. This provides a simple technique for
generating powerful upper bounds on the capacities of a general quantum
channel. We apply this technique to two qubit channels of particular
interest--the depolarizing channel and the channel with independent phase and
amplitude noise. Our study of the latter demonstrates that the key rate of BB84
with one-way post-processing and quantum bit error rate q cannot exceed
H(1/2-2q(1-q)) - H(2q(1-q)).Comment: 6 pages, one figur
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
Capacities of Quantum Amplifier Channels
Quantum amplifier channels are at the core of several physical processes. Not
only do they model the optical process of spontaneous parametric
down-conversion, but the transformation corresponding to an amplifier channel
also describes the physics of the dynamical Casimir effect in superconducting
circuits, the Unruh effect, and Hawking radiation. Here we study the
communication capabilities of quantum amplifier channels. Invoking a recently
established minimum output-entropy theorem for single-mode phase-insensitive
Gaussian channels, we determine capacities of quantum-limited amplifier
channels in three different scenarios. First, we establish the capacities of
quantum-limited amplifier channels for one of the most general communication
tasks, characterized by the trade-off between classical communication, quantum
communication, and entanglement generation or consumption. Second, we establish
capacities of quantum-limited amplifier channels for the trade-off between
public classical communication, private classical communication, and secret key
generation. Third, we determine the capacity region for a broadcast channel
induced by the quantum-limited amplifier channel, and we also show that a fully
quantum strategy outperforms those achieved by classical coherent detection
strategies. In all three scenarios, we find that the capacities significantly
outperform communication rates achieved with a naive time-sharing strategy.Comment: 16 pages, 2 figures, accepted for publication in Physical Review
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
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