428 research outputs found
Quantum trade-off coding for bosonic communication
The trade-off capacity region of a quantum channel characterizes the optimal
net rates at which a sender can communicate classical, quantum, and entangled
bits to a receiver by exploiting many independent uses of the channel, along
with the help of the same resources. Similarly, one can consider a trade-off
capacity region when the noiseless resources are public, private, and secret
key bits. In [Phys. Rev. Lett. 108, 140501 (2012)], we identified these
trade-off rate regions for the pure-loss bosonic channel and proved that they
are optimal provided that a longstanding minimum output entropy conjecture is
true. Additionally, we showed that the performance gains of a trade-off coding
strategy when compared to a time-sharing strategy can be quite significant. In
the present paper, we provide detailed derivations of the results announced
there, and we extend the application of these ideas to thermalizing and
amplifying bosonic channels. We also derive a "rule of thumb" for trade-off
coding, which determines how to allocate photons in a coding strategy if a
large mean photon number is available at the channel input. Our results on the
amplifying bosonic channel also apply to the "Unruh channel" considered in the
context of relativistic quantum information theory.Comment: 20 pages, 7 figures, v2 has a new figure and a proof that the regions
are optimal for the lossy bosonic channel if the entropy photon-number
inequality is true; v3, submission to Physical Review A (see related work at
http://link.aps.org/doi/10.1103/PhysRevLett.108.140501); v4, final version
accepted into Physical Review
Information trade-offs for optical quantum communication
Recent work has precisely characterized the achievable trade-offs between
three key information processing tasks---classical communication (generation or
consumption), quantum communication (generation or consumption), and shared
entanglement (distribution or consumption), measured in bits, qubits, and ebits
per channel use, respectively. Slices and corner points of this
three-dimensional region reduce to well-known protocols for quantum channels. A
trade-off coding technique can attain any point in the region and can
outperform time-sharing between the best-known protocols for accomplishing each
information processing task by itself. Previously, the benefits of trade-off
coding that had been found were too small to be of practical value (viz., for
the dephasing and the universal cloning machine channels). In this letter, we
demonstrate that the associated performance gains are in fact remarkably high
for several physically relevant bosonic channels that model free-space /
fiber-optic links, thermal-noise channels, and amplifiers. We show that
significant performance gains from trade-off coding also apply when trading
photon-number resources between transmitting public and private classical
information simultaneously over secret-key-assisted bosonic channels.Comment: 6 pages, 2 figures, see related, longer article at arXiv:1105.011
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
Strong converse for the classical capacity of the pure-loss bosonic channel
This paper strengthens the interpretation and understanding of the classical
capacity of the pure-loss bosonic channel, first established in [Giovannetti et
al., Physical Review Letters 92, 027902 (2004), arXiv:quant-ph/0308012]. In
particular, we first prove that there exists a trade-off between communication
rate and error probability if one imposes only a mean-photon number constraint
on the channel inputs. That is, if we demand that the mean number of photons at
the channel input cannot be any larger than some positive number N_S, then it
is possible to respect this constraint with a code that operates at a rate
g(\eta N_S / (1-p)) where p is the code's error probability, \eta\ is the
channel transmissivity, and g(x) is the entropy of a bosonic thermal state with
mean photon number x. We then prove that a strong converse theorem holds for
the classical capacity of this channel (that such a rate-error trade-off cannot
occur) if one instead demands for a maximum photon number constraint, in such a
way that mostly all of the "shadow" of the average density operator for a given
code is required to be on a subspace with photon number no larger than n N_S,
so that the shadow outside this subspace vanishes as the number n of channel
uses becomes large. Finally, we prove that a small modification of the
well-known coherent-state coding scheme meets this more demanding constraint.Comment: 18 pages, 1 figure; accepted for publication in Problems of
Information Transmissio
New lower bounds to the output entropy of multi-mode quantum Gaussian channels
We prove that quantum thermal Gaussian input states minimize the output
entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are
entanglement breaking and of the multi-mode quantum Gaussian phase
contravariant channels among all the input states with a given entropy. This is
the first time that this property is proven for a multi-mode channel without
restrictions on the input states. A striking consequence of this result is a
new lower bound on the output entropy of all the multi-mode quantum Gaussian
attenuators and amplifiers in terms of the input entropy. We apply this bound
to determine new upper bounds to the communication rates in two different
scenarios. The first is classical communication to two receivers with the
quantum degraded Gaussian broadcast channel. The second is the simultaneous
classical communication, quantum communication and entanglement generation or
the simultaneous public classical communication, private classical
communication and quantum key distribution with the Gaussian quantum-limited
attenuator
Strong converse rates for classical communication over thermal and additive noise bosonic channels
We prove that several known upper bounds on the classical capacity of thermal
and additive noise bosonic channels are actually strong converse rates. Our
results strengthen the interpretation of these upper bounds, in the sense that
we now know that the probability of correctly decoding a classical message
rapidly converges to zero in the limit of many channel uses if the
communication rate exceeds these upper bounds. In order for these theorems to
hold, we need to impose a maximum photon number constraint on the states input
to the channel (the strong converse property need not hold if there is only a
mean photon number constraint). Our first theorem demonstrates that Koenig and
Smith's upper bound on the classical capacity of the thermal bosonic channel is
a strong converse rate, and we prove this result by utilizing the structural
decomposition of a thermal channel into a pure-loss channel followed by an
amplifier channel. Our second theorem demonstrates that Giovannetti et al.'s
upper bound on the classical capacity of a thermal bosonic channel corresponds
to a strong converse rate, and we prove this result by relating success
probability to rate, the effective dimension of the output space, and the
purity of the channel as measured by the Renyi collision entropy. Finally, we
use similar techniques to prove that similar previously known upper bounds on
the classical capacity of an additive noise bosonic channel correspond to
strong converse rates.Comment: Accepted for publication in Physical Review A; minor changes in the
text and few reference
Strong converse for the classical capacity of optical quantum communication channels
We establish the classical capacity of optical quantum channels as a sharp
transition between two regimes---one which is an error-free regime for
communication rates below the capacity, and the other in which the probability
of correctly decoding a classical message converges exponentially fast to zero
if the communication rate exceeds the classical capacity. This result is
obtained by proving a strong converse theorem for the classical capacity of all
phase-insensitive bosonic Gaussian channels, a well-established model of
optical quantum communication channels, such as lossy optical fibers, amplifier
and free-space communication. The theorem holds under a particular
photon-number occupation constraint, which we describe in detail in the paper.
Our result bolsters the understanding of the classical capacity of these
channels and opens the path to applications, such as proving the security of
noisy quantum storage models of cryptography with optical links.Comment: 15 pages, final version accepted into IEEE Transactions on
Information Theory. arXiv admin note: text overlap with arXiv:1312.328
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