arXiv subjects

Caslav Brukner

Publications and source records attributed to Caslav Brukner.

At least 55 records · Page 3Linked to original sources

arXiv2009

Quantum Theory and Beyond: Is Entanglement Special?

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some features with quantum theory, such as probabilistic predictions for individual outcomes (indeterminism), the impossibility of information transfer faster than speed of light (no-signaling) or the impossibility of copying of unknown states (no-cloning). A vast majority of attempts to find physical principles behind quantum theory either fall short of deriving the theory uniquely from the principles or are based on abstract mathematical assumptions that require themselves a more conclusive physical motivation. Here, we show that classical probability theory and quantum theory can be reconstructed from three reasonable axioms: (1) (Information capacity) All systems with information carrying capacity of one bit are equivalent. (2) (Locality) The state of a composite system is completely determined by measurements on its subsystems. (3) (Reversibility) Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one. A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.

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arXiv2009

Bell's Inequalities: Foundations and Quantum Communication

Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hidden-variable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-that-light-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind better-than-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real meaning is, it will be demonstrated how quantum contextuality and violations of local realism can be used as useful resources in quantum information applications.

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arXiv2009

Quantum complementarity and logical indeterminacy

Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system. I will show that certain mathematical propositions on a d-valent function of a binary argument can be encoded in d-dimensional quantum states of mutually unbiased basis (MUB) sets, and truth values of the propositions can be tested in MUB measurements. I will then show that a proposition is undecidable within the system of axioms encoded in the state, if and only if the measurement associated with the proposition gives completely random outcomes.

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arXiv2009

Information Invariance and Quantum Probabilities

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory.

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arXiv2009

In the Kreisgang between classical and quantum physics

All our statements about the physical world are expressed in terms of everyday notions and thus in terms of classical physics. This necessity is behind each of our attempt to extract meaning out of empirical data and to communicate this knowledge to others. As such, it must apply also to the account of measurement arrangements and to the outcome in quantum experiments. On the other hand, however, if quantum mechanics is universally valid it should be possible to give a purely quantum mechanical description of objects of increasingly large sizes, eventually of the measurement devices themselves. It is suggested to resolve this dilemma by using the method of von Weizsaecker's circular and consistent movement in a reconstruction (Kreisgang) in which it is legitimate to recover the elements with which one started the reconstruction. The parameters entering the complex amplitudes of a quantum state have an operational meaning as parameters that specify the configuration of macroscopic instruments by which the state is prepared and measured. This classical aspect in each quantum description is at the "beginning" of the Kreisgang. The Kreisgang is "closed" by showing that under the every-day conditions of coarse-grained measurements a description of macroscopic instruments emerges in terminology of classical physics and the three-dimensional ordinary space from within quantum theory.

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arXiv2009

Positive phase space transformation incompatible with classical physics

Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is "when phase space measurements are performed". We introduce the theory-independent concept of "operationally local transformations" which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a positive Wigner function and performing only operationally local transformations that preserve this positivity, can nonetheless violate Bell's inequality. Such operationally local transformations are realized using entangled ancillae.

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arXiv2009

Monogamy of Bell's inequality violations in non-signaling theories

We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.

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arXiv2009

Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models

Mutually unbiased bases encapsulate the concept of complementarity - the impossibility of simultaneous knowledge of certain observables - in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.

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arXiv2008

Efficient Hidden-Variable Simulation of Measurements in Quantum Experiments

We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many measurements, our method gives models with the minimal number of hidden-variable states, which scales linearly with the number of measurements. These results can find applications in foundations of quantum theory, complexity studies and classical simulations of quantum systems.

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arXiv2008

Comment on: Testing the speed of 'spooky action at a distance'

In a recent experiment, Salart et al. addressed the important issues of the speed of hypothetical communication and of reference frames in Bell-type experiments. The authors report that they "performed a Bell experiment using entangled photons" and conclude from their experimental results that "to maintain an explanation based on spooky action at a distance we would have to assume that the spooky action propagates at speeds even greater than the bounds obtained in our experiment", exceeding the speed of light by orders of magnitude. Here we show that, analyzing the experimental procedure, explanations with subluminal or even no communication at all exist for the experiment.

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arXiv2008

The conditions for quantum violation of macroscopic realism

Why do we not experience a violation of macroscopic realism in every-day life? Normally, no violation can be seen either because of decoherence or the restriction of coarse-grained measurements, transforming the time evolution of any quantum state into a classical time evolution of a statistical mixture. We find the sufficient condition for these classical evolutions for spin systems under coarse-grained measurements. Then we demonstrate that there exist "non-classical" Hamiltonians whose time evolution cannot be understood classically, although at every instant of time the quantum spin state appears as a classical mixture. We suggest that such Hamiltonians are unlikely to be realized in nature because of their high computational complexity.

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arXiv2008

Heat Capacity as A Witness of Entanglement

We demonstrate that the presence of entanglement in macroscopic bodies (e.g. solids) in thermodynamical equilibrium could be revealed by measuring heat-capacity. The idea is that if the system were in a separable state, then for certain Hamiltonians heat capacity would not tend asymptotically to zero as the temperature approaches absolute zero. Since this would contradict the third law of thermodynamics, one concludes that the system must contain entanglement. The separable bounds are obtained by minimization of the heat capacity over separable states and using its universal low-temperature behavior. Our results open up a possibility to use standard experimental techniques of solid state physics -- namely, heat capacity measurements -- to detect entanglement in macroscopic samples.

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arXiv2008

Space-QUEST: Experiments with quantum entanglement in space

The European Space Agency (ESA) has supported a range of studies in the field of quantum physics and quantum information science in space for several years, and consequently we have submitted the mission proposal Space-QUEST (Quantum Entanglement for Space Experiments) to the European Life and Physical Sciences in Space Program. We propose to perform space-to-ground quantum communication tests from the International Space Station (ISS). We present the proposed experiments in space as well as the design of a space based quantum communication payload.

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arXiv2008

Photonic entanglement as a resource in quantum computation and quantum communication

Entanglement is an essential resource in current experimental implementations for quantum information processing. We review a class of experiments exploiting photonic entanglement, ranging from one-way quantum computing over quantum communication complexity to long-distance quantum communication. We then propose a set of feasible experiments that will underline the advantages of photonic entanglement for quantum information processing.

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arXiv2007

Classical world arising out of quantum physics under the restriction of coarse-grained measurements

Conceptually different from the decoherence program, we present a novel theoretical approach to macroscopic realism and classical physics within quantum theory. It focuses on the limits of observability of quantum effects of macroscopic objects, i.e., on the required precision of our measurement apparatuses such that quantum phenomena can still be observed. First, we demonstrate that for unrestricted measurement accuracy no classical description is possible for arbitrarily large systems. Then we show for a certain time evolution that under coarse-grained measurements not only macrorealism but even the classical Newtonian laws emerge out of the Schroedinger equation and the projection postulate.

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arXiv2007

An experimental test of non-local realism

Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.

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arXiv2006

Entanglement distribution revealed by macroscopic observations

What can we learn about entanglement between individual particles in macroscopic samples by observing only the collective properties of the ensembles? Using only a few experimentally feasible collective properties, we establish an entanglement measure between two samples of spin-1/2 particles (as representatives of two-dimensional quantum systems). This is a tight lower bound for the average entanglement between all pairs of spins in general and is equal to the average entanglement for a certain class of systems. We compute the entanglement measures for explicit examples and show how to generalize the method to more than two samples and multi-partite entanglement.

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arXiv2006

Experimental Entangled Entanglement

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally-entangled state. We show theoretically and experimentally, that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a CHSH-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled entanglement".

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