8,883 research outputs found
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
Information-theoretic aspects of the generalized amplitude damping channel
The generalized amplitude damping channel (GADC) is one of the sources of
noise in superconducting-circuit-based quantum computing. It can be viewed as
the qubit analogue of the bosonic thermal channel, and it thus can be used to
model lossy processes in the presence of background noise for low-temperature
systems. In this work, we provide an information-theoretic study of the GADC.
We first determine the parameter range for which the GADC is entanglement
breaking and the range for which it is anti-degradable. We then establish
several upper bounds on its classical, quantum, and private capacities. These
bounds are based on data-processing inequalities and the uniform continuity of
information-theoretic quantities, as well as other techniques. Our upper bounds
on the quantum capacity of the GADC are tighter than the known upper bound
reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the
entire parameter range of the GADC, thus reducing the gap between the lower and
upper bounds. We also establish upper bounds on the two-way assisted quantum
and private capacities of the GADC. These bounds are based on the squashed
entanglement, and they are established by constructing particular squashing
channels. We compare these bounds with the max-Rains information bound, the
mutual information bound, and another bound based on approximate covariance.
For all capacities considered, we find that a large variety of techniques are
useful in establishing bounds.Comment: 33 pages, 9 figures; close to the published versio
Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the \u27data-processing bound,\u27 is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel. We prove that the data-processing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel. We discuss another data-processing upper bound as well. Two other upper bounds, which we call the \u27ϵ-degradable bound\u27 and the \u27ϵ-close-degradable bound,\u27 are established using the notion of approximate degradability along with energy constraints. We find a strong limitation on any potential superadditivity of the coherent information of any phase-insensitive Gaussian channel in the low-noise regime, as the data-processing bound is very near to a known lower bound in such cases. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that make use of displaced thermal states. We end by proving that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint. What remains open for several interesting channel divergences, such as the diamond norm or the Rényi channel divergence, is to determine whether, among all input states, a Gaussian state is optimal
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
Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
As with classical information, error-correcting codes enable reliable
transmission of quantum information through noisy or lossy channels. In
contrast to the classical theory, imperfect quantum channels exhibit a strong
kind of synergy: there exist pairs of discrete memoryless quantum channels,
each of zero quantum capacity, which acquire positive quantum capacity when
used together. Here we show that this "superactivation" phenomenon also occurs
in the more realistic setting of optical channels with attenuation and Gaussian
noise. This paves the way for its experimental realization and application in
real-world communications systems.Comment: 5 pages, 4 figures, one appendi
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
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