129 research outputs found
coherent states and a Gaussian de Finetti theorem
We prove a generalization of the quantum de Finetti theorem when the local
space is an infinite-dimensional Fock space. In particular, instead of
considering the action of the permutation group on copies of that space, we
consider the action of the unitary group on the creation operators of
the modes and define a natural generalization of the symmetric subspace as
the space of states invariant under unitaries in . Our first result is a
complete characterization of this subspace, which turns out to be spanned by a
family of generalized coherent states related to the special unitary group
of signature . More precisely, this construction yields a
unitary representation of the noncompact simple real Lie group . We
therefore find a dual unitary representation of the pair of groups and
on an -mode Fock space.
The (Gaussian) coherent states resolve the identity on the
symmetric subspace, which implies a Gaussian de Finetti theorem stating that
tracing over a few modes of a unitary-invariant state yields a state close to a
mixture of Gaussian states. As an application of this de Finetti theorem, we
show that the upper-left submatrix of an Haar-invariant
unitary matrix is close in total variation distance to a matrix of independent
normal variables if .Comment: v2: 39 pages, including new application to truncations of Haar random
matrices. Comments are welcom
Composable security proof for continuous-variable quantum key distribution with coherent states
We give the first composable security proof for continuous-variable quantum
key distribution with coherent states against collective attacks. Crucially, in
the limit of large blocks the secret key rate converges to the usual value
computed from the Holevo bound. Combining our proof with either the de Finetti
theorem or the Postselection technique then shows the security of the protocol
against general attacks, thereby confirming the long-standing conjecture that
Gaussian attacks are optimal asymptotically in the composable security
framework.
We expect that our parameter estimation procedure, which does not rely on any
assumption, will find applications elsewhere, for instance for the reliable
quantification of continuous-variable entanglement in finite-size settings.Comment: 27 pages, 1 figure. v2: added a version of the AEP valid for
conditional state
Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations
The ability to distribute secret keys between two parties with
information-theoretic security, that is, regardless of the capacities of a
malevolent eavesdropper, is one of the most celebrated results in the field of
quantum information processing and communication. Indeed, quantum key
distribution illustrates the power of encoding information on the quantum
properties of light and has far reaching implications in high-security
applications. Today, quantum key distribution systems operate in real-world
conditions and are commercially available. As with most quantum information
protocols, quantum key distribution was first designed for qubits, the
individual quanta of information. However, the use of quantum continuous
variables for this task presents important advantages with respect to qubit
based protocols, in particular from a practical point of view, since it allows
for simple implementations that require only standard telecommunication
technology. In this review article, we describe the principle of
continuous-variable quantum key distribution, focusing in particular on
protocols based on coherent states. We discuss the security of these protocols
and report on the state-of-the-art in experimental implementations, including
the issue of side-channel attacks. We conclude with promising perspectives in
this research field.Comment: 21 pages, 2 figures, 1 tabl
Analysis of circuit imperfections in BosonSampling
BosonSampling is a problem where a quantum computer offers a provable speedup
over classical computers. Its main feature is that it can be solved with
current linear optics technology, without the need for a full quantum computer.
In this work, we investigate whether an experimentally realistic BosonSampler
can really solve BosonSampling without any fault-tolerance mechanism. More
precisely, we study how the unavoidable errors linked to an imperfect
calibration of the optical elements affect the final result of the computation.
We show that the fidelity of each optical element must be at least , where refers to the number of single photons in the scheme. Such
a requirement seems to be achievable with state-of-the-art equipment.Comment: 20 pages, 7 figures, v2: new title, to appear in QI
Information reconciliation for discretely-modulated continuous-variable quantum key distribution
The goal of this note is to explain the reconciliation problem for
continuous-variable quantum key distribution protocols with a discrete
modulation. Such modulation formats are attractive since they significantly
simplify experimental implementations compared to protocols with a Gaussian
modulation. Previous security proofs that relied crucially on the Gaussian
distribution of the input states are rendered inapplicable, and new proofs
based on the entropy accumulation theorem have emerged. Unfortunately, these
proofs are not compatible with existing reconciliation procedures, and
necessitate a reevaluation of the reconciliation problem. We argue that this
problem is nontrivial and deserves further attention. In particular, assuming
it can be solved with optimal efficiency leads to overly optimistic predictions
for the performance of the key distribution protocol, in particular for long
distances.Comment: 11 pages, 1 figur
Probabilistic models on contextuality scenarios
We introduce a framework to describe probabilistic models in Bell
experiments, and more generally in contextuality scenarios. Such a scenario is
a hypergraph whose vertices represent elementary events and hyperedges
correspond to measurements. A probabilistic model on such a scenario associates
to each event a probability, in such a way that events in a given measurement
have a total probability equal to one. We discuss the advantages of this
framework, like the unification of the notions of contexuality and nonlocality,
and give a short overview of results obtained elsewhere.Comment: In Proceedings QPL 2013, arXiv:1412.791
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