2,012 research outputs found
Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
In the literature on the continuous-variable bosonic teleportation protocol
due to [Braunstein and Kimble, Phys. Rev. Lett., 80(4):869, 1998], it is often
loosely stated that this protocol converges to a perfect teleportation of an
input state in the limit of ideal squeezing and ideal detection, but the exact
form of this convergence is typically not clarified. In this paper, I
explicitly clarify that the convergence is in the strong sense, and not the
uniform sense, and furthermore, that the convergence occurs for any input state
to the protocol, including the infinite-energy Basel states defined and
discussed here. I also prove, in contrast to the above result, that the
teleportation simulations of pure-loss, thermal, pure-amplifier, amplifier, and
additive-noise channels converge both strongly and uniformly to the original
channels, in the limit of ideal squeezing and detection for the simulations.
For these channels, I give explicit uniform bounds on the accuracy of their
teleportation simulations. I then extend these uniform convergence results to
particular multi-mode bosonic Gaussian channels. These convergence statements
have important implications for mathematical proofs that make use of the
teleportation simulation of bosonic Gaussian channels, some of which have to do
with bounding their non-asymptotic secret-key-agreement capacities. As a
byproduct of the discussion given here, I confirm the correctness of the proof
of such bounds from my joint work with Berta and Tomamichel from [Wilde,
Tomamichel, Berta, IEEE Trans. Inf. Theory 63(3):1792, March 2017].
Furthermore, I show that it is not necessary to invoke the energy-constrained
diamond distance in order to confirm the correctness of this proof.Comment: 19 pages, 3 figure
Quantum channels and their entropic characteristics
One of the major achievements of the recently emerged quantum information
theory is the introduction and thorough investigation of the notion of quantum
channel which is a basic building block of any data-transmitting or
data-processing system. This development resulted in an elaborated structural
theory and was accompanied by the discovery of a whole spectrum of entropic
quantities, notably the channel capacities, characterizing
information-processing performance of the channels. This paper gives a survey
of the main properties of quantum channels and of their entropic
characterization, with a variety of examples for finite dimensional quantum
systems. We also touch upon the "continuous-variables" case, which provides an
arena for quantum Gaussian systems. Most of the practical realizations of
quantum information processing were implemented in such systems, in particular
based on principles of quantum optics. Several important entropic quantities
are introduced and used to describe the basic channel capacity formulas. The
remarkable role of the specific quantum correlations - entanglement - as a
novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys.
(in press
Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
A bipartite quantum interaction corresponds to the most general quantum
interaction that can occur between two quantum systems in the presence of a
bath. In this work, we determine bounds on the capacities of bipartite
interactions for entanglement generation and secret key agreement between two
quantum systems. Our upper bound on the entanglement generation capacity of a
bipartite quantum interaction is given by a quantity called the bidirectional
max-Rains information. Our upper bound on the secret-key-agreement capacity of
a bipartite quantum interaction is given by a related quantity called the
bidirectional max-relative entropy of entanglement. We also derive tighter
upper bounds on the capacities of bipartite interactions obeying certain
symmetries. Observing that reading of a memory device is a particular kind of
bipartite quantum interaction, we leverage our bounds from the bidirectional
setting to deliver bounds on the capacity of a task that we introduce, called
private reading of a wiretap memory cell. Given a set of point-to-point quantum
wiretap channels, the goal of private reading is for an encoder to form
codewords from these channels, in order to establish secret key with a party
who controls one input and one output of the channels, while a passive
eavesdropper has access to one output of the channels. We derive both lower and
upper bounds on the private reading capacities of a wiretap memory cell. We
then extend these results to determine achievable rates for the generation of
entanglement between two distant parties who have coherent access to a
controlled point-to-point channel, which is a particular kind of bipartite
interaction.Comment: v3: 34 pages, 3 figures, accepted for publication in Physical Review
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
Semidefinite programming relaxations for quantum correlations
Semidefinite programs are convex optimisation problems involving a linear
objective function and a domain of positive semidefinite matrices. Over the
last two decades, they have become an indispensable tool in quantum information
science. Many otherwise intractable fundamental and applied problems can be
successfully approached by means of relaxation to a semidefinite program. Here,
we review such methodology in the context of quantum correlations. We discuss
how the core idea of semidefinite relaxations can be adapted for a variety of
research topics in quantum correlations, including nonlocality, quantum
communication, quantum networks, entanglement, and quantum cryptography.Comment: To be submitted to Reviews of Modern Physic
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