123 research outputs found
Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
The squashed entanglement of a quantum channel is an additive function of
quantum channels, which finds application as an upper bound on the rate at
which secret key and entanglement can be generated when using a quantum channel
a large number of times in addition to unlimited classical communication. This
quantity has led to an upper bound of on the capacity
of a pure-loss bosonic channel for such a task, where is the average
fraction of photons that make it from the input to the output of the channel.
The purpose of the present paper is to extend these results beyond the
single-sender single-receiver setting to the more general case of a single
sender and multiple receivers (a quantum broadcast channel). We employ
multipartite generalizations of the squashed entanglement to constrain the
rates at which secret key and entanglement can be generated between any subset
of the users of such a channel, along the way developing several new properties
of these measures. We apply our results to the case of a pure-loss broadcast
channel with one sender and two receivers.Comment: 35 pages, 1 figure, accepted for publication in IEEE Transactions on
Information Theor
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
Unconstrained distillation capacities of a pure-loss bosonic broadcast channel
Bosonic channels are important in practice as they form a simple model for
free-space or fiber-optic communication. Here we consider a single-sender
two-receiver pure-loss bosonic broadcast channel and determine the
unconstrained capacity region for the distillation of bipartite entanglement
and secret key between the sender and each receiver, whenever they are allowed
arbitrary public classical communication. We show how the state merging
protocol leads to achievable rates in this setting, giving an inner bound on
the capacity region. We also evaluate an outer bound on the region by using the
relative entropy of entanglement and a `reduction by teleportation' technique.
The outer bounds match the inner bounds in the infinite-energy limit, thereby
establishing the unconstrained capacity region for such channels. Our result
could provide a useful benchmark for implementing a broadcasting of
entanglement and secret key through such channels. An important open question
relevant to practice is to determine the capacity region in both this setting
and the single-sender single-receiver case when there is an energy constraint
on the transmitter.Comment: v2: 6 pages, 3 figures, introduction revised, appendix added where
the result is extended to the 1-to-m pure-loss bosonic broadcast channel. v3:
minor revision, typo error correcte
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
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
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