740 research outputs found
Quantum broadcast channels
We consider quantum channels with one sender and two receivers, used in
several different ways for the simultaneous transmission of independent
messages. We begin by extending the technique of superposition coding to
quantum channels with a classical input to give a general achievable region. We
also give outer bounds to the capacity regions for various special cases from
the classical literature and prove that superposition coding is optimal for a
class of channels. We then consider extensions of superposition coding for
channels with a quantum input, where some of the messages transmitted are
quantum instead of classical, in the sense that the parties establish bipartite
or tripartite GHZ entanglement. We conclude by using state merging to give
achievable rates for establishing bipartite entanglement between different
pairs of parties with the assistance of free classical communication.Comment: 15 pages; IEEE Trans. Inform. Theory, vol. 57, no. 10, October 201
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
Energy-constrained two-way assisted private and quantum capacities of quantum channels
With the rapid growth of quantum technologies, knowing the fundamental
characteristics of quantum systems and protocols is essential for their
effective implementation. A particular communication setting that has received
increased focus is related to quantum key distribution and distributed quantum
computation. In this setting, a quantum channel connects a sender to a
receiver, and their goal is to distill either a secret key or entanglement,
along with the help of arbitrary local operations and classical communication
(LOCC). In this work, we establish a general theory of energy-constrained,
LOCC-assisted private and quantum capacities of quantum channels, which are the
maximum rates at which an LOCC-assisted quantum channel can reliably establish
secret key or entanglement, respectively, subject to an energy constraint on
the channel input states. We prove that the energy-constrained squashed
entanglement of a channel is an upper bound on these capacities. We also
explicitly prove that a thermal state maximizes a relaxation of the squashed
entanglement of all phase-insensitive, single-mode input bosonic Gaussian
channels, generalizing results from prior work. After doing so, we prove that a
variation of the method introduced in [Goodenough et al., New J. Phys. 18,
063005 (2016)] leads to improved upper bounds on the energy-constrained
secret-key-agreement capacity of a bosonic thermal channel. We then consider a
multipartite setting and prove that two known multipartite generalizations of
the squashed entanglement are in fact equal. We finally show that the
energy-constrained, multipartite squashed entanglement plays a role in bounding
the energy-constrained LOCC-assisted private and quantum capacity regions of
quantum broadcast channels.Comment: 31 pages, 6 figure
Applications of position-based coding to classical communication over quantum channels
Recently, a coding technique called position-based coding has been used to
establish achievability statements for various kinds of classical communication
protocols that use quantum channels. In the present paper, we apply this
technique in the entanglement-assisted setting in order to establish lower
bounds for error exponents, lower bounds on the second-order coding rate, and
one-shot lower bounds. We also demonstrate that position-based coding can be a
powerful tool for analyzing other communication settings. In particular, we
reduce the quantum simultaneous decoding conjecture for entanglement-assisted
or unassisted communication over a quantum multiple access channel to open
questions in multiple quantum hypothesis testing. We then determine achievable
rate regions for entanglement-assisted or unassisted classical communication
over a quantum multiple-access channel, when using a particular quantum
simultaneous decoder. The achievable rate regions given in this latter case are
generally suboptimal, involving differences of Renyi-2 entropies and
conditional quantum entropies.Comment: v4: 44 pages, v4 includes a simpler proof for an upper bound on
one-shot entanglement-assisted capacity, also found recently and
independently in arXiv:1804.0964
Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
Previous work on the classical information capacities of bosonic channels has
established the capacity of the single-user pure-loss channel, bounded the
capacity of the single-user thermal-noise channel, and bounded the capacity
region of the multiple-access channel. The latter is a multi-user scenario in
which several transmitters seek to simultaneously and independently communicate
to a single receiver. We study the capacity region of the bosonic broadcast
channel, in which a single transmitter seeks to simultaneously and
independently communicate to two different receivers. It is known that the
tightest available lower bound on the capacity of the single-user thermal-noise
channel is that channel's capacity if, as conjectured, the minimum von Neumann
entropy at the output of a bosonic channel with additive thermal noise occurs
for coherent-state inputs. Evidence in support of this minimum output entropy
conjecture has been accumulated, but a rigorous proof has not been obtained. In
this paper, we propose a new minimum output entropy conjecture that, if proved
to be correct, will establish that the capacity region of the bosonic broadcast
channel equals the inner bound achieved using a coherent-state encoding and
optimum detection. We provide some evidence that supports this new conjecture,
but again a full proof is not available.Comment: 13 pages, 7 figure
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