16 research outputs found
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
Maximal quantum randomness in Bell tests
The non-local correlations exhibited when measuring entangled particles can
be used to certify the presence of genuine randomness in Bell experiments.
While non-locality is necessary for randomness certification, it is unclear
when and why non-locality certifies maximal randomness. We provide here a
simple argument to certify the presence of maximal local and global randomness
based on symmetries of a Bell inequality and the existence of a unique quantum
probability distribution that maximally violates it. Using our findings, we
prove the existence of N-party Bell test attaining maximal global randomness,
that is, where a combination of measurements by each party provides N perfect
random bits.Comment: 5 pages, 1 figur
Geographic variation of surface energy partitioning in the climatic mean predicted from the maximum power limit
Convective and radiative cooling are the two principle mechanisms by which
the Earth's surface transfers heat into the atmosphere and that shape surface
temperature. However, this partitioning is not sufficiently constrained by
energy and mass balances alone. We use a simple energy balance model in which
convective fluxes and surface temperatures are determined with the additional
thermodynamic limit of maximum convective power. We then show that the broad
geographic variation of heat fluxes and surface temperatures in the
climatological mean compare very well with the ERA-Interim reanalysis over land
and ocean. We also show that the estimates depend considerably on the
formulation of longwave radiative transfer and that a spatially uniform offset
is related to the assumed cold temperature sink at which the heat engine
operates.Comment: 17 pages, 3 figures, 2 table
Can observed randomness be certified to be fully intrinsic?
Randomness comes in two qualitatively different forms. Apparent randomness
can result both from ignorance or lack of control of degrees of freedom in the
system. In contrast, intrinsic randomness should not be ascribable to any such
cause. While classical systems only possess the first kind of randomness,
quantum systems are believed to exhibit some intrinsic randomness. In general,
any observed random process includes both forms of randomness. In this work, we
provide quantum processes in which all the observed randomness is fully
intrinsic. These results are derived under minimal assumptions: the validity of
the no-signalling principle and an arbitrary (but not absolute) lack of freedom
of choice. The observed randomness tends to a perfect random bit when
increasing the number of parties, thus defining an explicit process attaining
full randomness amplification.Comment: 4 pages + appendice
A New Relation between post and pre-optimal measurement states
When an optimal measurement is made on a qubit and what we call an Unbiased
Mixture of the resulting ensembles is taken, then the post measurement density
matrix is shown to be related to the pre-measurement density matrix through a
simple and linear relation. It is shown that such a relation holds only when
the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is
also shown explicitly that non-orthogonal measurements fail to give such a
linear relation no matter how the ensembles are mixed. The result has been
proved to be true for arbitrary quantum mechanical systems of finite
dimensional Hilbert spaces. The result is true irrespective of whether the
initial state is pure or mixed.Comment: 4 pages in REVTE
Certifying the Absence of Apparent Randomness under Minimal Assumptions
Contrary to classical physics, the predictions of quantum theory for measurement outcomes are of a probabilistic nature. Questions about the completeness of such predictions lie at the core of quantum physics and can be traced back to the foundations of the field. Recently, the completeness of quantum probabilistic predictions could be established based on the assumption of freedom of choice. Here we ask when can events be established to be as unpredictable as we observe them to be relying only on minimal assumptions, ie. distrusting even the free choice assumption but assuming the existence of an arbitrarily weak (but non-zero) source of randomness. We answer the latter by identifying a sufficient condition weaker than the monogamy of correlations which allow us to provide a family of finite scenarios based on GHZ paradoxes where quantum probabilistic predictions are as accurate as they can possibly be. Our results can be used for a protocol of full randomness amplification, without the need of privacy amplification, in which the final bit approaches a perfect random bit exponentially fast on the number of parties
Full randomness from arbitrarily deterministic events
Do completely unpredictable events exist? Classical physics excludes
fundamental randomness. Although quantum theory makes probabilistic
predictions, this does not imply that nature is random, as randomness should
be certified without relying on the complete structure of the theory being
used. Bell tests approach the question from this perspective. However, they
require prior perfect randomness, falling into a circular reasoning. A Bell
test that generates perfect random bits from bits possessing high—but less
than perfect—randomness has recently been obtained. Yet, the main question
remained open: does any initial randomness suffice to certify perfect
randomness? Here we show that this is indeed the case. We provide a Bell test
that uses arbitrarily imperfect random bits to produce bits that are, under
the non-signalling principle assumption, perfectly random. This provides the
first protocol attaining full randomness amplification. Our results have
strong implications onto the debate of whether there exist events that are
fully random