161 research outputs found
Mermin Non-Locality in Abstract Process Theories
The study of non-locality is fundamental to the understanding of quantum
mechanics. The past 50 years have seen a number of non-locality proofs, but its
fundamental building blocks, and the exact role it plays in quantum protocols,
has remained elusive. In this paper, we focus on a particular flavour of
non-locality, generalising Mermin's argument on the GHZ state. Using strongly
complementary observables, we provide necessary and sufficient conditions for
Mermin non-locality in abstract process theories. We show that the existence of
more phases than classical points (aka eigenstates) is not sufficient, and that
the key to Mermin non-locality lies in the presence of certain algebraically
non-trivial phases. This allows us to show that fRel, a favourite toy model for
categorical quantum mechanics, is Mermin local. We show Mermin non-locality to
be the key resource ensuring the device-independent security of the HBB CQ
(N,N) family of Quantum Secret Sharing protocols. Finally, we challenge the
unspoken assumption that the measurements involved in Mermin-type scenarios
should be complementary (like the pair X,Y), opening the doors to a much wider
class of potential experimental setups than currently employed. In short, we
give conditions for Mermin non-locality tests on any number of systems, where
each party has an arbitrary number of measurement choices, where each
measurement has an arbitrary number of outcomes and further, that works in any
abstract process theory.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments
If noncontextuality is defined as the robustness of a system's response to a
measurement against other simultaneous measurements, then the Kochen-Specker
arguments do not provide an algebraic proof for quantum contextuality. Namely,
for the argument to be effective, (i) each operator must be uniquely associated
with a measurement and (ii) commuting operators must represent simultaneous
measurements. However, in all Kochen-Specker arguments discussed in the
literature either (i) or (ii) is not met. Arguments meeting (i) contain at
least one subset of mutually commuting operators which do not represent
simultaneous measurements and hence fail to physically justify the functional
composition principle. Arguments meeting (ii) associate some operators with
more than one measurement and hence need to invoke an extra assumption
different from noncontextuality.Comment: 27 pages, 1 figur
Categorical Quantum Dynamics
We use strong complementarity to introduce dynamics and symmetries within the
framework of CQM, which we also extend to infinite-dimensional separable
Hilbert spaces: these were long-missing features, which open the way to a
wealth of new applications. The coherent treatment presented in this work also
provides a variety of novel insights into the dynamics and symmetries of
quantum systems: examples include the extremely simple characterisation of
symmetry-observable duality, the connection of strong complementarity with the
Weyl Canonical Commutation Relations, the generalisations of Feynman's clock
construction, the existence of time observables and the emergence of quantum
clocks.
Furthermore, we show that strong complementarity is a key resource for
quantum algorithms and protocols. We provide the first fully diagrammatic,
theory-independent proof of correctness for the quantum algorithm solving the
Hidden Subgroup Problem, and show that strong complementarity is the feature
providing the quantum advantage. In quantum foundations, we use strong
complementarity to derive the exact conditions relating non-locality to the
structure of phase groups, within the context of Mermin-type non-locality
arguments. Our non-locality results find further application to quantum
cryptography, where we use them to define a quantum-classical secret sharing
scheme with provable device-independent security guarantees.
All in all, we argue that strong complementarity is a truly powerful and
versatile building block for quantum theory and its applications, and one that
should draw a lot more attention in the future.Comment: Thesis submitted for the degree of Doctor of Philosophy, Oxford
University, Michaelmas Term 2016 (273 pages
Quantum Bayesianism Assessed
The idea that the quantum probabilities are best construed as the personal/subjective degrees of belief of Bayesian agents is an old one. In recent years the idea has been vigorously pursued by a group of physicists who fly the banner of quantum Bayesianism (QBism). The present paper aims to identify the prospects and problems of implementing QBism, and it critically assesses the claim that QBism provides a resolution (or dissolution) of some of the long standing foundations issues in quantum mechanics, including the measurement problem and puzzles of non-localit
Intrinsic randomness in non-local theories: quantification and amplification
Quantum mechanics was developed as a response to the inadequacy of classical physics in explaining certain physical phenomena. While it has proved immensely successful, it also presents several features that severely challenge our classicality based intuition. Randomness in quantum theory is one such and is the central theme of this dissertation.
Randomness is a notion we have an intuitive grasp on since it appears to abound in nature. It a icts weather systems and nancial markets and is explicitly used in sport and gambling. It is used in a wide range of scienti c applications such as the simulation of genetic drift, population dynamics and molecular motion in fluids. Randomness (or the lack of it) is also central to philosophical concerns such as the existence of free will and anthropocentric notions of ethics and morality. The conception of randomness has evolved dramatically along with physical theory. While all randomness in classical theory can be fully attributed to a lack of knowledge of the observer, quantum theory qualitatively departs by allowing the existence of objective or intrinsic randomness. It is now known that intrinsic randomness is a generic feature of hypothetical theories larger than quantum theory called the non-signalling theories. They are usually studied with regards to a potential future completion of quantum mechanics or from the perspective of recognizing new physical principles describing nature. While several aspects have been studied to date, there has been little work in globally characterizing and quantifying randomness in quantum and non-signalling theories and the relationship between them. This dissertation is an attempt to ll this gap. Beginning with the unavoidable assumption of a weak source of randomness in the universe, we characterize upper bounds on quantum and non-signalling randomness. We develop a simple symmetry argument that helps identify maximal randomness in quantum theory and demonstrate its use in several explicit examples. Furthermore, we show that maximal randomness is forbidden within general non-signalling theories and constitutes a quantitative departure from quantum theory. We next address (what was) an open question about randomness ampli cation. It is known that a single source of randomness cannot be ampli ed using classical resources alone. We show that using quantum resources on the
other hand allows a full ampli cation of the weakest sources of randomness to maximal randomness even in the presence of supra-quantum adversaries. The signi cance of this result spans practical cryptographic scenarios as well as foundational concerns. It demonstrates that conditional on the smallest set of assumptions, the existence of the weakest randomness in the universe guarantees the existence of maximal randomness. The next question we address is the quanti cation of intrinsic randomness in non-signalling correlations. While this is intractable in general, we identify cases where this can be quanti ed. We nd that in these cases all observed randomness is intrinsic even relaxing the measurement independence assumption. We nally turn to the study of the only known resource that allows generating certi able intrinsic randomness in the laboratory i.e. entanglement. We address noisy quantum systems and calculate their entanglement dynamics under decoherence. We identify exact results for several realistic noise models and provide tight bounds in some other cases. We conclude by putting our results into perspective, pointing out some drawbacks and future avenues of work in addressing these concerns
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