Entanglement between Collective Operators in a Linear Harmonic Chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several non-contiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.Comment: 7 pages, 4 figures, significantly revised version with new results, journal reference adde

Experimenter's Freedom in Bell's Theorem and Quantum Cryptography

Bell's theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings. Within a local realistic picture the violation of Bell's inequalities can only be understood if this freedom is denied. We determine the minimal degree to which the experimenter's freedom has to be abandoned, if one wants to keep such a picture and be in agreement with the experiment. Furthermore, the freedom in choosing experimental arrangements may be considered as a resource, since its lacking can be used by an eavesdropper to harm the security of quantum communication. We analyze the security of quantum key distribution as a function of the (partial) knowledge the eavesdropper has about the future choices of measurement settings which are made by the authorized parties (e.g. on the basis of some quasi-random generator). We show that the equivalence between the violation of Bell's inequality and the efficient extraction of a secure key - which exists for the case of complete freedom (no setting knowledge) - is lost unless one adapts the bound of the inequality according to this lack of freedom.Comment: 7 pages, 2 figures, incorporated referee comment

Addressing the clumsiness loophole in a Leggett-Garg test of macrorealism

The rise of quantum information theory has lent new relevance to experimental tests for non-classicality, particularly in controversial cases such as adiabatic quantum computing superconducting circuits. The Leggett-Garg inequality is a "Bell inequality in time" designed to indicate whether a single quantum system behaves in a macrorealistic fashion. Unfortunately, a violation of the inequality can only show that the system is either (i) non-macrorealistic or (ii) macrorealistic but subjected to a measurement technique that happens to disturb the system. The "clumsiness" loophole (ii) provides reliable refuge for the stubborn macrorealist, who can invoke it to brand recent experimental and theoretical work on the Leggett-Garg test inconclusive. Here, we present a revised Leggett-Garg protocol that permits one to conclude that a system is either (i) non-macrorealistic or (ii) macrorealistic but with the property that two seemingly non-invasive measurements can somehow collude and strongly disturb the system. By providing an explicit check of the invasiveness of the measurements, the protocol replaces the clumsiness loophole with a significantly smaller "collusion" loophole.Comment: 7 pages, 3 figure

Mitochondrial DNA mutations in renal cell carcinomas revealed no general impact on energy metabolism

Previously, renal cell carcinoma tissues were reported to display a marked reduction of components of the respiratory chain. To elucidate a possible relationship between tumourigenesis and alterations of oxidative phosphorylation, we screened for mutations of the mitochondrial DNA (mtDNA) in renal carcinoma tissues and patient-matched normal kidney cortex. Seven of the 15 samples investigated revealed at least one somatic heteroplasmic mutation as determined by denaturating HPLC analysis (DHPLC). No homoplasmic somatic mutations were observed. Actually, half of the mutations presented a level of heteroplasmy below 25%, which could be easily overlooked by automated sequence analysis. The somatic mutations included four known D-loop mutations, four so far unreported mutations in ribosomal genes, one synonymous change in the ND4 gene and four nonsynonymous base changes in the ND2, COI, ND5 and ND4L genes. One renal cell carcinoma tissue showed a somatic A3243G mutation, which is a known frequent cause of MELAS syndrome (mitochondrial encephalomyopathy, lactic acidosis, stroke-like episode) and specific compensatory alterations of enzyme activities of the respiratory chain in the tumour tissue. No difference between histopathology and clinical progression compared to the other tumour tissues was observed. In conclusion, the low abundance as well as the frequently observed low level of heteroplasmy of somatic mtDNA mutations indicates that the decreased aerobic energy capacity in tumour tissue seems to be mediated by a general nuclear regulated mechanism

Multiplex primer extension analysis for rapid detection of major European mitochondrial haplogroups

The evolution of the human mitochondrial genome is reflected in the existence of eth- nically distinct lineages or haplogroups. Alterations of mitochondrial DNA (mtDNA) have been instrumental in studies of human phylogeny, in population genetics, and in molecular medicine to link pathological mutations to a variety of human diseases of complex etiology. For each of these applications, rapid and cost effective assays for mtDNA haplogrouping are invaluable. Here we describe a hierarchical system for mtDNA haplogrouping that combines multiplex PCR amplifications, multiplex single- base primer extensions, and CE for analyzing ten haplogroup-diagnostic mitochondrial single nucleotide polymorphisms. Using this rapid and cost-effective mtDNA geno- typing method, we were able to show that within a large, randomly selected cohort of healthy Austrians ( n = 1172), mtDNAs could be assigned to all nine major European haplogroups. Forty-four percent belonged to haplogroup H, the most frequent hap- logroup in European Caucasian populations. The other major haplogroups identified were U (15.4%), J (11.8%), T (8.2%) and K (5.1%). The frequencies of haplogroups in Austria is within the range observed for other European countries. Our method may be suitable for mitochondrial genotyping of samples from large-scale epidemiology stud- ies and for identifying markers of genetic susceptibility

Entanglement between smeared field operators in the Klein-Gordon vacuum

Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.Comment: 21 pages, 11 figure

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

Quantum models of classical mechanics: maximum entropy packets

In a previous paper, a project of constructing quantum models of classical properties has been started. The present paper concludes the project by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of the state operators of ME packets is obtained with its help. The diagonal representation of the operators is found. A general way of calculating averages that can replace the partition function method is described. Classical mechanics is reinterpreted as a statistical theory. Classical trajectories are replaced by classical ME packets. Quantum states approximate classical ones if the product of the coordinate and momentum variances is much larger than Planck constant. Thus, ME packets with large variances follow their classical counterparts better than Gaussian wave packets.Comment: 26 pages, no figure. Introduction and the section on classical limit are extended, new references added. Definitive version accepted by Found. Phy