56 research outputs found
Simple, near-optimal quantum protocols for die-rolling
Die-rolling is the cryptographic task where two mistrustful, remote parties
wish to generate a random -sided die-roll over a communication channel.
Optimal quantum protocols for this task have been given by Aharon and Silman
(New Journal of Physics, 2010) but are based on optimal weak coin-flipping
protocols which are currently very complicated and not very well understood. In
this paper, we first present very simple classical protocols for die-rolling
which have decent (and sometimes optimal) security which is in stark contrast
to coin-flipping, bit-commitment, oblivious transfer, and many other two-party
cryptographic primitives. We also present quantum protocols based on
integer-commitment, a generalization of bit-commitment, where one wishes to
commit to an integer. We analyze these protocols using semidefinite programming
and finally give protocols which are very close to Kitaev's lower bound for any
. Lastly, we briefly discuss an application of this work to the
quantum state discrimination problem.Comment: v2. Updated titl
Device-independent dimension test in a multiparty Bell experiment
A device-independent dimension test for a Bell experiment aims to estimate
the underlying Hilbert space dimension that is required to produce given
measurement statistical data without any other assumptions concerning the
quantum apparatus. Previous work mostly deals with the two-party version of
this problem. In this paper, we propose a very general and robust approach to
test the dimension of any subsystem in a multiparty Bell experiment. Our
dimension test stems from the study of a new multiparty scenario which we call
prepare-and-distribute. This is like the prepare-and-measure scenario, but the
quantum state is sent to multiple, non-communicating parties. Through specific
examples, we show that our test results can be tight. Furthermore, we compare
the performance of our test to results based on known bipartite tests, and
witness remarkable advantage, which indicates that our test is of a true
multiparty nature. We conclude by pointing out that with some partial
information about the quantum states involved in the experiment, it is possible
to learn other interesting properties beyond dimension.Comment: 10 pages, 2 figure
How to make unforgeable money in generalised probabilistic theories
We discuss the possibility of creating money that is physically impossible to
counterfeit. Of course, "physically impossible" is dependent on the theory that
is a faithful description of nature. Currently there are several proposals for
quantum money which have their security based on the validity of quantum
mechanics. In this work, we examine Wiesner's money scheme in the framework of
generalised probabilistic theories. This framework is broad enough to allow for
essentially any potential theory of nature, provided that it admits an
operational description. We prove that under a quantifiable version of the
no-cloning theorem, one can create physical money which has an exponentially
small chance of being counterfeited. Our proof relies on cone programming, a
natural generalisation of semidefinite programming. Moreover, we discuss some
of the difficulties that arise when considering non-quantum theories.Comment: 27 pages, many diagrams. Comments welcom
Strong connections between quantum encodings, non-locality and quantum cryptography
Encoding information in quantum systems can offer surprising advantages but
at the same time there are limitations that arise from the fact that measuring
an observable may disturb the state of the quantum system. In our work, we
provide an in-depth analysis of a simple question: What happens when we perform
two measurements sequentially on the same quantum system? This question touches
upon some fundamental properties of quantum mechanics, namely the uncertainty
principle and the complementarity of quantum measurements. Our results have
interesting consequences, for example they can provide a simple proof of the
optimal quantum strategy in the famous Clauser-Horne-Shimony-Holt game.
Moreover, we show that the way information is encoded in quantum systems can
provide a different perspective in understanding other fundamental aspects of
quantum information, like non-locality and quantum cryptography. We prove some
strong equivalences between these notions and provide a number of applications
in all areas.Comment: Version 3. Previous title: "Oblivious transfer, the CHSH game, and
quantum encodings
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