9,933 research outputs found
Fundamental rate-loss tradeoff for optical quantum key distribution
Since 1984, various optical quantum key distribution (QKD) protocols have
been proposed and examined. In all of them, the rate of secret key generation
decays exponentially with distance. A natural and fundamental question is then
whether there are yet-to-be discovered optical QKD protocols (without quantum
repeaters) that could circumvent this rate-distance tradeoff. This paper
provides a major step towards answering this question. We show that the
secret-key-agreement capacity of a lossy and noisy optical channel assisted by
unlimited two-way public classical communication is limited by an upper bound
that is solely a function of the channel loss, regardless of how much optical
power the protocol may use. Our result has major implications for understanding
the secret-key-agreement capacity of optical channels---a long-standing open
problem in optical quantum information theory---and strongly suggests a real
need for quantum repeaters to perform QKD at high rates over long distances.Comment: 9+4 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1310.012
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
The squashed entanglement of a quantum channel
This paper defines the squashed entanglement of a quantum channel as the
maximum squashed entanglement that can be registered by a sender and receiver
at the input and output of a quantum channel, respectively. A new subadditivity
inequality for the original squashed entanglement measure of Christandl and
Winter leads to the conclusion that the squashed entanglement of a quantum
channel is an additive function of a tensor product of any two quantum
channels. More importantly, this new subadditivity inequality, along with prior
results of Christandl, Winter, et al., establishes the squashed entanglement of
a quantum channel as an upper bound on the quantum communication capacity of
any channel assisted by unlimited forward and backward classical communication.
A similar proof establishes this quantity as an upper bound on the private
capacity of a quantum channel assisted by unlimited forward and backward public
classical communication. This latter result is relevant as a limitation on
rates achievable in quantum key distribution. As an important application, we
determine that these capacities can never exceed log((1+eta)/(1-eta)) for a
pure-loss bosonic channel for which a fraction eta of the input photons make it
to the output on average. The best known lower bound on these capacities is
equal to log(1/(1-eta)). Thus, in the high-loss regime for which eta << 1, this
new upper bound demonstrates that the protocols corresponding to the above
lower bound are nearly optimal.Comment: v3: 25 pages, 3 figures, significant expansion of paper; v2: error in
a prior version corrected (main result unaffected), cited Tucci for his work
related to squashed entanglement; 5 + epsilon pages and 2-page appendi
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