21,484 research outputs found
Automated Verification of Quantum Protocols using MCMAS
We present a methodology for the automated verification of quantum protocols
using MCMAS, a symbolic model checker for multi-agent systems The method is
based on the logical framework developed by D'Hondt and Panangaden for
investigating epistemic and temporal properties, built on the model for
Distributed Measurement-based Quantum Computation (DMC), an extension of the
Measurement Calculus to distributed quantum systems. We describe the
translation map from DMC to interpreted systems, the typical formalism for
reasoning about time and knowledge in multi-agent systems. Then, we introduce
dmc2ispl, a compiler into the input language of the MCMAS model checker. We
demonstrate the technique by verifying the Quantum Teleportation Protocol, and
discuss the performance of the tool.Comment: In Proceedings QAPL 2012, arXiv:1207.055
Quantum Measurements from a Logical Point of View
We introduce a logic modelling some aspects of the behaviour of the
measurement process, in such a way that no direct mention of quantum states is
made, thus avoiding the problems associated to this rather evasive notion. We
then study some properties of the models of this logic, and deduce some
characteristics that any model (and hence, any formulation of quantum mechanics
compatible with its predictions and relying on a notion of measurement) should
verify. The main results we obtain are that in the case of a Hilbert space of
dimension at least 3, using a strengthening of the Kochen-Specker theorem, we
show that no model can lead to the certain prediction of more than one atomic
outcome. Moreover, if the Hilbert space is finite dimensional, then we are able
to precisely describe the structure of the predictions of any model of our
logic. In particular, we show that all the models of our logic do exactly make
the same predictions regarding whether a given sequence of outcomes is possible
or not, so that quantum mechanics can be considered complete as long as the
possibility of outcomes is considered.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Logical Bell Inequalities
Bell inequalities play a central role in the study of quantum non-locality
and entanglement, with many applications in quantum information. Despite the
huge literature on Bell inequalities, it is not easy to find a clear conceptual
answer to what a Bell inequality is, or a clear guiding principle as to how
they may be derived. In this paper, we introduce a notion of logical Bell
inequality which can be used to systematically derive testable inequalities for
a very wide variety of situations. There is a single clear conceptual
principle, based on purely logical consistency conditions, which underlies our
notion of logical Bell inequalities. We show that in a precise sense, all Bell
inequalities can be taken to be of this form. Our approach is very general. It
applies directly to any family of sets of commuting observables. Thus it covers
not only the n-partite scenarios to which Bell inequalities are standardly
applied, but also Kochen-Specker configurations, and many other examples. There
is much current work on experimental tests for contextuality. Our approach
directly yields, in a systematic fashion, testable inequalities for a very
general notion of contextuality.
There has been much work on obtaining proofs of Bell's theorem `without
inequalities' or `without probabilities'. These proofs are seen as being in a
sense more definitive and logically robust than the inequality-based proofs. On
the hand, they lack the fault-tolerant aspect of inequalities. Our approach
reconciles these aspects, and in fact shows how the logical robustness can be
converted into systematic, general derivations of inequalities with provable
violations. Moreover, the kind of strong non-locality or contextuality
exhibited by the GHZ argument or by Kochen-Specker configurations can be shown
to lead to maximal violations of the corresponding logical Bell inequalities.Comment: 12 page
Experimental Test of Two-way Quantum Key Distribution in Presence of Controlled Noise
We describe the experimental test of a quantum key distribution performed
with a two-way protocol without using entanglement. An individual incoherent
eavesdropping is simulated and induces a variable amount of noise on the
communication channel. This allows a direct verification of the agreement
between theory and practice.Comment: 4 pages, 3 figure
Quantum Non-Objectivity from Performativity of Quantum Phenomena
We analyze the logical foundations of quantum mechanics (QM) by stressing
non-objectivity of quantum observables which is a consequence of the absence of
logical atoms in QM. We argue that the matter of quantum non-objectivity is
that, on the one hand, the formalism of QM constructed as a mathematical theory
is self-consistent, but, on the other hand, quantum phenomena as results of
experimenter's performances are not self-consistent. This self-inconsistency is
an effect of that the language of QM differs much from the language of human
performances. The first is the language of a mathematical theory which uses
some Aristotelian and Russellian assumptions (e.g., the assumption that there
are logical atoms). The second language consists of performative propositions
which are self-inconsistent only from the viewpoint of conventional
mathematical theory, but they satisfy another logic which is non-Aristotelian.
Hence, the representation of quantum reality in linguistic terms may be
different: from a mathematical theory to a logic of performative propositions.
To solve quantum self-inconsistency, we apply the formalism of non-classical
self-referent logics
- …