40 research outputs found
Tight asymptotic key rate for the BB84 protocol with local randomisation and device imprecisions
Local randomisation is a preprocessing procedure in which one of the
legitimate parties of a quantum key distribution (QKD) scheme adds noise to
their version of the key and was found by Kraus et al. [Phys. Rev. Lett. 95,
080501 (2005)] to improve the security of certain QKD protocols. In this
article, the improvement yielded by local randomisation is derived for an
imperfect implementation of the BB84 QKD protocol, in which the source emits
four given but arbitrary pure states and the detector performs
arbitrarily-aligned measurements. Specifically, this is achieved by modifying
an approach to analysing the security of imperfect variants of the BB84
protocol against collective attacks, introduced in [Phys. Rev. A 88, 012331
(2013)], to include the additional preprocessing step. The previously known
improvement to the threshold channel noise, from 11\% to 12.41\%, is recovered
in the special case of an ideal BB84 implementation and becomes more pronounced
in the case of a nonideal source. Finally, the bound derived for the asymptotic
key rate, both with and without local randomisation, is shown to be tight with
the particular source characterisation used. This is demonstrated by the
explicit construction of a family of source states and optimal attacks for
which the key-rate bound is attained with equality
Effects of preparation and measurement misalignments on the security of the BB84 quantum key distribution protocol
The ideal Bennett-Brassard 1984 (BB84) quantum key distribution protocol is
based on the preparation and measurement of qubits in two alternative bases
differing by an angle of pi/2. Any real implementation of the protocol, though,
will inevitably introduce misalignments in the preparation of the states and in
the alignment of the measurement bases with respect to this ideal situation.
Various security proofs take into account (at least partially) such errors,
i.e., show how Alice and Bob can still distil a secure key in the presence of
these imperfections. Here, we consider the complementary problem: how can Eve
exploit misalignments to obtain more information about the key than would be
possible in an ideal implementation? Specifically, we investigate the effects
of misalignment errors on the security of the BB84 protocol in the case of
individual attacks, where necessary and sufficient conditions for security are
known. Though the effects of these errors are small for expected deviations
from the perfect situation, our results nevertheless show that Alice and Bob
can incorrectly conclude that they have established a secure key if the
inevitable experimental errors in the state preparation and in the alignment of
the measurements are not taken into account. This gives further weight to the
idea that the formulation and security analysis of any quantum cryptography
protocol should be based on realistic assumptions about the properties of the
apparatus used. Additionally, we note that BB84 seems more robust against
alignment imperfections if both the x and z bases are used to generate the key
Device-independent tests of structures of measurement incompatibility
In contrast with classical physics, in quantum physics some sets of
measurements are incompatible in the sense that they can not be performed
simultaneously. Among other applications, incompatibility allows for
contextuality and Bell nonlocality. This makes of crucial importance developing
tools for certifying whether a set of measurements posses a certain structure
of incompatibility. Here we show that, for quantum or nonsignaling models, if
the measurements employed in a Bell test satisfy a given type of compatibility,
then the amount of violation of some specific Bell inequalities become limited.
Then, we show that correlations arising from local measurements on two-qubit
states violate these limits, which rules out in a device-independent way such
structures of incompatibility. In particular, we prove that quantum
correlations allow for a device-independent demonstration of genuine triplewise
incompatibility. Finally, we translate these results into a
semi-device-independent Einstein-Podolsky-Rosen-steering scenario.Comment: Substantial improvements, several new results added, new author
added. 18 pages, 4 figure
Randomness versus nonlocality in the Mermin-Bell experiment with three parties
The detection of nonlocal correlations in a Bell experiment implies almost by
definition some intrinsic randomness in the measurement outcomes. For given
correlations, or for a given Bell violation, the amount of randomness predicted
by quantum physics, quantified by the guessing probability, can generally be
bounded numerically. However, currently only a few exact analytic solutions are
known for violations of the bipartite Clauser-Horne-Shimony-Holt Bell
inequality. Here, we study the randomness in a Bell experiment where three
parties test the tripartite Mermin-Bell inequality. We give tight upper bounds
on the guessing probabilities associated with one and two of the parties'
measurement outcomes as a function of the Mermin inequality violation. Finally,
we discuss the possibility of device-independent secret sharing based on the
Mermin inequality and argue that the idea seems unlikely to work
Device-independent quantum key distribution with asymmetric CHSH inequalities
The simplest device-independent quantum key distribution protocol is based on
the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and allows two users,
Alice and Bob, to generate a secret key if they observe sufficiently strong
correlations. There is, however, a mismatch between the protocol, in which only
one of Alice's measurements is used to generate the key, and the CHSH
expression, which is symmetric with respect to Alice's two measurements. We
therefore investigate the impact of using an extended family of Bell
expressions where we give different weights to Alice's measurements. Using this
family of asymmetric Bell expressions improves the robustness of the key
distribution protocol for certain experimentally-relevant correlations. As an
example, the tolerable error rate improves from 7.15% to about 7.42% for the
depolarising channel. Adding random noise to Alice's key before the
postprocessing pushes the threshold further to more than 8.34%. The main
technical result of our work is a tight bound on the von Neumann entropy of one
of Alice's measurement outcomes conditioned on a quantum eavesdropper for the
family of asymmetric CHSH expressions we consider and allowing for an arbitrary
amount of noise preprocessing
Device-independent quantum key distribution with single-photon sources
Device-independent quantum key distribution protocols allow two honest users
to establish a secret key with minimal levels of trust on the provider, as
security is proven without any assumption on the inner working of the devices
used for the distribution. Unfortunately, the implementation of these protocols
is challenging, as it requires the observation of a large Bell-inequality
violation between the two distant users. Here, we introduce novel photonic
protocols for device-independent quantum key distribution exploiting
single-photon sources and heralding-type architectures. The heralding process
is designed so that transmission losses become irrelevant for security. We then
show how the use of single-photon sources for entanglement distribution in
these architectures, instead of standard entangled-pair generation schemes,
provides significant improvements on the attainable key rates and distances
over previous proposals. Given the current progress in single-photon sources,
our work opens up a promising avenue for device-independent quantum key
distribution implementations.Comment: 20 pages (9 + appendices and bibliography), 5 figures, 1 tabl
Maximal randomness from partially-entangled states
We investigate how much randomness can be extracted from a generic
partially-entangled pure state of two qubits in a device-independent setting,
where a Bell test is used to certify the correct functioning of the apparatus.
For any such state, we first show that two bits of randomness are always
attainable both if projective measurements are used to generate the randomness
globally or if a non-projective measurement is used to generate the randomness
locally. We then prove that the maximum amount of randomness that can be
generated using non-projective measurements globally is restricted to between
approximately 3.58 and 3.96 bits. The upper limit rules out that a bound of
four bits potentially obtainable with extremal qubit measurements can be
attained. We point out this is a consequence of the fact that non-projective
qubit measurements with four outcomes can only be self-tested to a limited
degree in a Bell experiment
Characterising correlations under informational restrictions
The strength of correlations observed between two separated events hinges on
the amount of information transmitted between them. We characterise the
correlations that can be created in classical and quantum experiments which
feature a given amount of communicated information. For classical models, we
present a complete characterisation of informationally restricted correlations
in terms of linear programming. For quantum models, we develop a hierarchy of
increasingly precise semidefinite relaxations to bound the set of
informationally restricted quantum correlations. We leverage these techniques
to i) derive device-independent witnesses of the information content of quantum
communication, ii) the derivation of strict inequalities for different quantum
information resources and iii) a new avenue for semi-device-independent random
number generation based on the information assumption.Comment: First versio
Semi-device-independent framework based on natural physical assumptions
The semi-device-independent approach provides a framework for
prepare-and-measure quantum protocols using devices whose behavior must not be
characterized nor trusted, except for a single assumption on the dimension of
the Hilbert space characterizing the quantum carriers. Here, we propose instead
to constrain the quantum carriers through a bound on the mean value of a
well-chosen observable. This modified assumption is physically better motivated
than a dimension bound and closer to the description of actual experiments. In
particular, we consider quantum optical schemes where the source emits quantum
states described in an infinite-dimensional Fock space and model our assumption
as an upper bound on the average photon number in the emitted states. We
characterize the set of correlations that may be exhibited in the simplest
possible scenario compatible with our new framework, based on two
energy-constrained state preparations and a two-outcome measurement.
Interestingly, we uncover the existence of quantum correlations exceeding the
set of classical correlations that can be produced by devices behaving in a
purely pre-determined fashion (possibly including shared randomness). This
feature suggests immediate applications to certified randomness generation.
Along this line, we analyze the achievable correlations in several
prepare-and-measure optical schemes with a mean photon number constraint and
demonstrate that they allow for the generation of certified randomness. Our
simplest optical scheme works by the on-off keying of an attenuated laser
source followed by photocounting. It opens the path to more sophisticated
energy-constrained semi-device-independent quantum cryptography protocols, such
as quantum key distribution.Comment: 26 pages, 10 figure