1,205 research outputs found
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
Code designs for MIMO broadcast channels
Recent information-theoretic results show the optimality of dirty-paper coding (DPC) in achieving the full capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This paper presents a DPC based code design for BCs. We consider the case in which there is an individual rate/signal-to-interference-plus-noise ratio (SINR) constraint for each user. For a fixed transmitter power, we choose the linear transmit precoding matrix such that the SINRs at users are uniformly maximized, thus ensuring the best bit-error rate performance. We start with Cover's simplest two-user Gaussian BC and present a coding scheme that operates 1.44 dB from the boundary of the capacity region at the rate of one bit per real sample (b/s) for each user. We then extend the coding strategy to a two-user MIMO Gaussian BC with two transmit antennas at the base-station and develop the first limit-approaching code design using nested turbo codes for DPC. At the rate of 1 b/s for each user, our design operates 1.48 dB from the capacity region boundary. We also consider the performance of our scheme over a slow fading BC. For two transmit antennas, simulation results indicate a performance loss of only 1.4 dB, 1.64 dB and 1.99 dB from the theoretical limit in terms of the total transmission power for the two, three and four user case, respectively
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