On the solution of trivalent decision problems by quantum state identification

The trivalent functions of a trit can be grouped into equipartitions of three elements. We discuss the separation of the corresponding functional classes by quantum state identifications

Bell's experiment with intra- and inter-pair entanglement: Single-particle mode entanglement as a case study

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large many-body system where all the pairs are generally entangled with each other. Using an explicit example based on single mode entanglement and an ancillary Bose-Einstein condensate, we show that the Bell-inequality violation in such systems can display statistical properties that are remarkably different from those obtained using identically prepared, independent pairs. In particular, one can have probabilistic violation of Bell's inequalities in which a finite fraction of all the runs result in violation, even though there could be no violation when averaging over all the runs. Whether or not a particular run of results will end up being local realistically explainable is "decided" by a sequence of quantum (random) outcomes.Comment: 7 pages (two column), 5 figure

Information and The Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.Comment: 20 pages, two figures, last version. Section 4 is replaced by a new argument. Other sections are improved. An appendix and new references are adde

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.Comment: 4 pages, 1 figure, second revised and published versio

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.Comment: 4 pages, 2 figures, revised version, journal reference adde

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental appendi

Crucial Role of Quantum Entanglement in Bulk Properties of Solids

We demonstrate that the magnetic susceptibility of strongly alternating antiferromagnetic spin-1/2 chains is an entanglement witness. Specifically, magnetic susceptibility of copper nitrate (CN) measured in 1963 (Berger et al., Phys. Rev. 132, 1057 (1963)) cannot be described without presence of entanglement. A detailed analysis of the spin correlations in CN as obtained from neutron scattering experiments (Xu et al., Phys. Rev. Lett. 84, 4465 (2000)) provides microscopic support for this interpretation. We present a quantitative analysis resulting in the critical temperature of 5K in both, completely independent, experiments below which entanglement exists.Comment: 4 pages, 2 figure

Quantum nonlocality obtained from local states by entanglement purification

We have applied an entanglement purification protocol to produce a single entangled pair of photons capable of violating a CHSH Bell inequality from two pairs that individually could not. The initial poorly-entangled photons were created by a controllable decoherence that introduced complex errors. All of the states were reconstructed using quantum state tomography which allowed for a quantitative description of the improvement of the state after purification.Comment: 4 pages, 4 figure

A scheme for entanglement extraction from a solid

Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However this entanglement may appear a mere mathematical artifact of the typical symmetrization procedure of many-body wave function in solid state physics. Here we show that this entanglement is physical demonstrating the principles of its extraction from a typical solid state system by scattering two particles off the system. Moreover we show how to simulate this process using present-day optical lattices technology. This demonstrates not only that entanglement exists in solids but also that it can be used for quantum information processing or for test of Bell's inequalities.Comment: 10 pages, 3 figures, published versio