669 research outputs found
Optimality of Gaussian Attacks in Continuous Variable Quantum Cryptography
We analyze the asymptotic security of the family of Gaussian modulated
Quantum Key Distribution protocols for Continuous Variables systems. We prove
that the Gaussian unitary attack is optimal for all the considered bounds on
the key rate when the first and second momenta of the canonical variables
involved are known by the honest parties.Comment: See also R. Garcia-Patron and N. Cerf, quant-ph/060803
Tight bound on coherent states quantum key distribution with heterodyne detection
We propose a new upper bound for the eavesdropper's information in the direct
and reverse reconciliated coherent states quantum key distribution protocols
with heterodyne detection. This bound is derived by maximizing the leaked
information over the symplectic group of transformations that spans every
physical Gaussian attack on individual pulses. We exhibit four different
attacks that reach this bound, which shows that this bound is tight. Finally,
we compare the secret key rate obtained with this new bound to the homodyne
rate.Comment: 8 pages, 3 figure
A symmetrization technique for continuous-variable quantum key distribution
We introduce a symmetrization technique which can be used as an extra step in
some continuous-variable quantum key distribution protocols. By randomizing the
data in phase space, one can dramatically simplify the security analysis of the
protocols, in particular in the case of collective attacks. The main
application of this procedure concerns protocols with postselection, for which
security was established only against Gaussian attacks until now. Here, we
prove that under some experimentally verifiable conditions, Gaussian attacks
are optimal among all collective attacks.Comment: 7 page
Robust and Efficient Sifting-Less Quantum Key Distribution Protocols
We show that replacing the usual sifting step of the standard
quantum-key-distribution protocol BB84 by a one-way reverse reconciliation
procedure increases its robustness against photon-number-splitting (PNS)
attacks to the level of the SARG04 protocol while keeping the raw key-rate of
BB84. This protocol, which uses the same state and detection than BB84, is the
m=4 member of a protocol-family using m polarization states which we introduce
here. We show that the robustness of these protocols against PNS attacks
increases exponentially with m, and that the effective keyrate of optimized
weak coherent pulses decreases with the transmission T like T^{1+1/(m-2)}
Virtual noiseless amplification and Gaussian post-selection in continuous-variable quantum key distribution
The noiseless amplification or attenuation are two heralded filtering
operations that enable respectively to increase or decrease the mean field of
any quantum state of light with no added noise, at the cost of a small success
probability. We show that inserting such noiseless operations in a transmission
line improves the performance of continuous-variable quantum key distribution
over this line. Remarkably, these noiseless operations do not need to be
physically implemented but can simply be simulated in the data post-processing
stage. Hence, virtual noiseless amplification or attenuation amounts to perform
a Gaussian post-selection, which enhances the secure range or tolerable excess
noise while keeping the benefits of Gaussian security proofs.Comment: 8 pages, 5 figure
Continuous Variable Quantum Cryptography using Two-Way Quantum Communication
Quantum cryptography has been recently extended to continuous variable
systems, e.g., the bosonic modes of the electromagnetic field. In particular,
several cryptographic protocols have been proposed and experimentally
implemented using bosonic modes with Gaussian statistics. Such protocols have
shown the possibility of reaching very high secret-key rates, even in the
presence of strong losses in the quantum communication channel. Despite this
robustness to loss, their security can be affected by more general attacks
where extra Gaussian noise is introduced by the eavesdropper. In this general
scenario we show a "hardware solution" for enhancing the security thresholds of
these protocols. This is possible by extending them to a two-way quantum
communication where subsequent uses of the quantum channel are suitably
combined. In the resulting two-way schemes, one of the honest parties assists
the secret encoding of the other with the chance of a non-trivial superadditive
enhancement of the security thresholds. Such results enable the extension of
quantum cryptography to more complex quantum communications.Comment: 12 pages, 7 figures, REVTe
Heisenberg-limited eavesdropping on the continuous-variable quantum cryptographic protocol with no basis switching is impossible
The Gaussian quantum key distribution protocol based on coherent states and
heterodyne detection [Phys. Rev. Lett. 93, 170504 (2004)] has the advantage
that no active random basis switching is needed on the receiver's side. Its
security is, however, not very satisfyingly understood today because the bounds
on the secret key rate that have been derived from Heisenberg relations are not
attained by any known scheme. Here, we address the problem of the optimal
Gaussian individual attack against this protocol, and derive tight upper bounds
on the information accessible to an eavesdropper. The optical scheme achieving
this bound is also exhibited, which concludes the security analysis of this
protocol.Comment: 10 pages, 6 figure
Virtual Entanglement and Reconciliation Protocols for Quantum Cryptography with Continuous Variables
We discuss quantum key distribution protocols using quantum continuous
variables. We show that such protocols can be made secure against individual
gaussian attacks regardless the transmission of the optical line between Alice
and Bob. This is achieved by reversing the reconciliation procedure subsequent
to the quantum transmission, that is, using Bob's instead of Alice's data to
build the key. Although squeezing or entanglement may be helpful to improve the
resistance to noise, they are not required for the protocols to remain secure
with high losses. Therefore, these protocols can be implemented very simply by
transmitting coherent states and performing homodyne detection. Here, we show
that entanglement nevertheless plays a crucial role in the security analysis of
coherent state protocols. Every cryptographic protocol based on displaced
gaussian states turns out to be equivalent to an entanglement-based protocol,
even though no entanglement is actually present. This equivalence even holds in
the absence of squeezing, for coherent state protocols. This ``virtual''
entanglement is important to assess the security of these protocols as it
provides an upper bound on the mutual information between Alice and Bob if they
had used entanglement. The resulting security criteria are compared to the
separability criterion for bipartite gaussian variables. It appears that the
security thresholds are well within the entanglement region. This supports the
idea that coherent state quantum cryptography may be unconditionally secure.Comment: 18 pages, 6 figures. Submitted to QI
Security of continuous-variable quantum key distribution against general attacks
We prove the security of Gaussian continuous-variable quantum key
distribution against arbitrary attacks in the finite-size regime. The novelty
of our proof is to consider symmetries of quantum key distribution in phase
space in order to show that, to good approximation, the Hilbert space of
interest can be considered to be finite-dimensional, thereby allowing for the
use of the postselection technique introduced by Christandl, Koenig and Renner
(Phys. Rev. Lett. 102, 020504 (2009)). Our result greatly improves on previous
work based on the de Finetti theorem which could not provide security for
realistic, finite-size, implementations.Comment: 5 pages, plus 11 page appendi
Gaussian Post-selection for Continuous Variable Quantum Cryptography
We extend the security proof for continuous variable quantum key distribution
protocols using post selection to account for arbitrary eavesdropping attacks
by employing the concept of an equivalent protocol where the post-selection is
implemented as a series of quantum operations including a virtual distillation.
We introduce a particular `Gaussian' post selection and demonstrate that the
security can be calculated using only experimentally accessible quantities.
Finally we explicitly evaluate the performance for the case of a noisy Gaussian
channel in the limit of unbounded key length and find improvements over all
pre-existing continuous variable protocols in realistic regimes.Comment: 4+4 pages. arXiv admin note: substantial text overlap with
arXiv:1106.082
- …