777 research outputs found
Multipartite Bound Information exists and can be activated
We prove the conjectured existence of Bound Information, a classical analog
of bound entanglement, in the multipartite scenario. We give examples of
tripartite probability distributions from which it is impossible to extract any
kind of secret key, even in the asymptotic regime, although they cannot be
created by local operations and public communication. Moreover, we show that
bound information can be activated: three honest parties can distill a common
secret key from different distributions having bound information. Our results
demonstrate that quantum information theory can provide useful insight for
solving open problems in classical information theory.Comment: four page
Multipartite Classical and Quantum Secrecy Monotones
In order to study multipartite quantum cryptography, we introduce quantities
which vanish on product probability distributions, and which can only decrease
if the parties carry out local operations or carry out public classical
communication. These ``secrecy monotones'' therefore measure how much secret
correlations are shared by the parties. In the bipartite case we show that the
mutual information is a secrecy monotone. In the multipartite case we describe
two different generalisations of the mutual information, both of which are
secrecy monotones. The existence of two distinct secrecy monotones allows us to
show that in multipartite quantum cryptography the parties must make
irreversible choices about which multipartite correlations they want to obtain.
Secrecy monotones can be extended to the quantum domain and are then defined on
density matrices. We illustrate this generalisation by considering tri-partite
quantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We
show that before carrying out measurements on the state, the parties must make
an irreversible decision about what probability distribution they want to
obtain
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
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
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