980 research outputs found
Hierarchy of efficiently computable and faithful lower bounds to quantum discord
Quantum discord expresses a fundamental non-classicality of correlations more
general than quantum entanglement. We combine the no-local-broadcasting
theorem, semidefinite-programming characterizations of quantum fidelity and
quantum separability, and a recent breakthrough result of Fawzi and Renner
about quantum Markov chains to provide a hierarchy of computationally efficient
lower bounds to quantum discord. Such a hierarchy converges to the surprisal of
measurement recoverability introduced by Seshadreesan and Wilde, and provides a
faithful lower bound to quantum discord already at the lowest non-trivial
level. Furthermore, the latter constitutes by itself a valid discord-like
measure of the quantumness of correlations.Comment: 7 pages, 2 figures; comments -- also about "extendable" Vs
"extendible" -- welcom
Upper bounds on secret key agreement over lossy thermal bosonic channels
Upper bounds on the secret-key-agreement capacity of a quantum channel serve
as a way to assess the performance of practical quantum-key-distribution
protocols conducted over that channel. In particular, if a protocol employs a
quantum repeater, achieving secret-key rates exceeding these upper bounds is a
witness to having a working quantum repeater. In this paper, we extend a recent
advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the
teleportation simulation of single-mode phase-insensitive Gaussian channels
such that it now applies to the relative entropy of entanglement measure. As a
consequence of this extension, we find tighter upper bounds on the
non-asymptotic secret-key-agreement capacity of the lossy thermal bosonic
channel than were previously known. The lossy thermal bosonic channel serves as
a more realistic model of communication than the pure-loss bosonic channel,
because it can model the effects of eavesdropper tampering and imperfect
detectors. An implication of our result is that the previously known upper
bounds on the secret-key-agreement capacity of the thermal channel are too
pessimistic for the practical finite-size regime in which the channel is used a
finite number of times, and so it should now be somewhat easier to witness a
working quantum repeater when using secret-key-agreement capacity upper bounds
as a benchmark.Comment: 16 pages, 1 figure, minor change
Multi-party Quantum Computation
We investigate definitions of and protocols for multi-party quantum computing
in the scenario where the secret data are quantum systems. We work in the
quantum information-theoretic model, where no assumptions are made on the
computational power of the adversary. For the slightly weaker task of
verifiable quantum secret sharing, we give a protocol which tolerates any t <
n/4 cheating parties (out of n). This is shown to be optimal. We use this new
tool to establish that any multi-party quantum computation can be securely
performed as long as the number of dishonest players is less than n/6.Comment: Masters Thesis. Based on Joint work with Claude Crepeau and Daniel
Gottesman. Full version is in preparatio
A universe of processes and some of its guises
Our starting point is a particular `canvas' aimed to `draw' theories of
physics, which has symmetric monoidal categories as its mathematical backbone.
In this paper we consider the conceptual foundations for this canvas, and how
these can then be converted into mathematical structure. With very little
structural effort (i.e. in very abstract terms) and in a very short time span
the categorical quantum mechanics (CQM) research program has reproduced a
surprisingly large fragment of quantum theory. It also provides new insights
both in quantum foundations and in quantum information, and has even resulted
in automated reasoning software called `quantomatic' which exploits the
deductive power of CQM. In this paper we complement the available material by
not requiring prior knowledge of category theory, and by pointing at
connections to previous and current developments in the foundations of physics.
This research program is also in close synergy with developments elsewhere, for
example in representation theory, quantum algebra, knot theory, topological
quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World
through Mathematical Innovation", H. Halvorson, ed., Cambridge University
Press, forthcoming. (as usual, many pictures
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
A resource theory of quantum memories and their faithful verification with minimal assumptions
We provide a complete set of game-theoretic conditions equivalent to the
existence of a transformation from one quantum channel into another one, by
means of classically correlated pre/post processing maps only. Such conditions
naturally induce tests to certify that a quantum memory is capable of storing
quantum information, as opposed to memories that can be simulated by
measurement and state preparation (corresponding to entanglement-breaking
channels). These results are formulated as a resource theory of genuine quantum
memories (correlated in time), mirroring the resource theory of entanglement in
quantum states (correlated spatially). As the set of conditions is complete,
the corresponding tests are faithful, in the sense that any non
entanglement-breaking channel can be certified. Moreover, they only require the
assumption of trusted inputs, known to be unavoidable for quantum channel
verification. As such, the tests we propose are intrinsically different from
the usual process tomography, for which the probes of both the input and the
output of the channel must be trusted. An explicit construction is provided and
shown to be experimentally realizable, even in the presence of arbitrarily
strong losses in the memory or detectors.Comment: Addition of a quantitative study of memories as resources, and
reformulated part of the results in that ligh
Photonic entanglement as a resource in quantum computation and quantum communication
Entanglement is an essential resource in current experimental implementations
for quantum information processing. We review a class of experiments exploiting
photonic entanglement, ranging from one-way quantum computing over quantum
communication complexity to long-distance quantum communication. We then
propose a set of feasible experiments that will underline the advantages of
photonic entanglement for quantum information processing.Comment: 33 pages, 4 figures, OSA styl
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