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Sep 21, 2013
09/13

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Mladen Pavicic

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We present an experiment which prepare entanglement between photons that nowhere interacted and whose paths nowhere crossed. The experiment puts together two photons from two (non-maximal) singlet-like photon pairs and make them interfere at an asymmetrical beam splitter. As a result one finds polarization correlations between the other companion photons from the pairs whose paths nowhere crossed each other even when no polarization measurements have been carried out on the former photons. The...

Source: http://arxiv.org/abs/quant-ph/9907038v1

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Sep 19, 2013
09/13

by
Mladen Pavicic

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We present a probabilistic (ideally 50%) nondestructive interaction-free atom-photon controlled-NOT gate, where nondestructive means that all four outgoing target photon modes of the gate are available and feed-forwardable. Individual atoms are controlled by a stimulated Raman adiabatic passage transition and photons by a ring resonator with two outgoing ports. Realistic estimates we obtain for ions confined in a Paul trap around which the resonator is mounted show that a strong atom-photon...

Source: http://arxiv.org/abs/0708.2302v1

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Sep 17, 2013
09/13

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Mladen Pavicic

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We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on a quantum system. In doing so we use MMP diagrams and linear algorithms. MMP diagrams are tractable since an n-block of an MMP diagram has n elements while an n-block of a standard lattice diagram has 2^n elements. An immediate test for such an approach is a...

Source: http://arxiv.org/abs/quant-ph/0207003v1

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Sep 23, 2013
09/13

by
Mladen Pavicic

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The original versions (1 and 2) of this paper paper contain a fatal error. All my attempts to patch the error have failed. As a service to the community I explain the error in some detail.

Source: http://arxiv.org/abs/1111.4273v3

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Sep 21, 2013
09/13

by
Mladen Pavicic

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It is shown that a monolithic total-internal-reflection resonator can be used for energy-exchange-free detections of objects without recoils. Related energy-exchange-free detection of "welcher Weg" is discussed and an experiment with an atom interferometer is proposed. The obtained results are in agreement with quantum theory.

Source: http://arxiv.org/abs/quant-ph/9907040v1

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Sep 21, 2013
09/13

by
Mladen Pavicic

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Spin interferometry of the 4th order for independent polarized as well as unpolarized photons arriving simultaneously at a beam splitter and exhibiting spin correlation while leaving it, is formulated and discussed in the quantum approach. Beam splitter is recognized as a source of genuine singlet photon states. Also, typical nonclassical beating between photons taking part in the interference of the 4th order is given a polarization dependent explanation.

Source: http://arxiv.org/abs/quant-ph/9907072v1

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Sep 24, 2013
09/13

by
Mladen Pavicic

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Algorithms for finding arbitrary sets of Kochen-Specker (KS) qunits (n-level systems) as well as all the remaining vectors in a space of an arbitrary dimension are presented. The algorithms are based on linear MMP diagrams which generate orthogonalities of KS qunits, on an algebraic definition of states on the diagrams, and on nonlinear equations corresponding to MMP diagrams whose solutions are either KS qunits or the remaining vectors of a chosen space depending on whether the diagrams allow...

Source: http://arxiv.org/abs/quant-ph/0412197v1

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Sep 21, 2013
09/13

by
Mladen Pavicic

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We discuss a scheme for a full superdense coding of entangled photon states employing only linear-optics elements. By using the mixed basis consisting of four states that are unambiguously distinguishable by a standard and polarizing beam splitters we can deterministically transfer four messages by manipulating just one of the two entangled photons. The sender achieves the determinism of the transfer either by giving up the control over 50% of sent messages (although known to her) or by...

Source: http://arxiv.org/abs/1104.1802v3

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Sep 17, 2013
09/13

by
Mladen Pavicic

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We propose a kind of reverse Kochen-Specker theorem that amounts to generating orthomodular lattices (OMLs) with exactly one state that do not admit properties of the Hilbert space. We apply MMP algorithms to obtain smallest OMLs with 35 atoms and 35 blocks (35-35) and all other ones up to 38-38. We find out that all but one of them admit exactly one state and discover several other properties of theirs. Previously known such OMLs have 44 atoms and 44 blocks or more. We present some of them in...

Source: http://arxiv.org/abs/1003.0233v1

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Sep 23, 2013
09/13

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Mladen Pavicic

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A nonclassical feature of the fourth-order interference at a beam splitter, that genuine photon spin singlets are emitted in predetermined directions even when incident photons are unpolarized, has been used in a proposal for an experiment that imposes quantum spin correlation on truly independent photons. In the experiment, two photons from two such singlets interfere at a beam splitter, and as a result the other two photons - which nowhere interacted and whose paths nowhere crossed - exhibit...

Source: http://arxiv.org/abs/quant-ph/9908024v1

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Jun 29, 2018
06/18

by
Mladen Pavicic

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We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical logic which turns out to have disjoint distributive and non-distributive ortholattices as its models. In particular, we prove that both classical and quantum logics are sound and complete with respect to each of these lattices. We also show that there is one...

Topics: Quantum Physics, Mathematical Physics, Logic, Mathematics

Source: http://arxiv.org/abs/1609.00822

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Sep 21, 2013
09/13

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Mladen Pavicic

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A method for preparing a loophole-free four-photon Bell experiments which requires a detection efficiency of 67% is proposed. It enables realistic detection efficiencies of 75% at a visibility of 85%. Two type-II crystals each down convert one correlated photon pair and we entangle one photon from one pair with one photon from the other pair on a highly transparent beam splitter. The entanglement selects two other conjugate photons into a Bell state. Wide solid angles for the conjugate photons...

Source: http://arxiv.org/abs/quant-ph/9907039v1

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Jul 20, 2013
07/13

by
Harry Paul; Mladen Pavicic

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We propose a realistic device for detecting objects almost without transferring a single quantum of energy to them. The device can work with an efficiency close to 100% and relies on two detectors counting both presence and absence of the objects. Its possible usage in performing fundamental experiments as well as possible applications are discussed.

Source: http://arxiv.org/abs/quant-ph/9906102v2

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Sep 23, 2013
09/13

by
Harry Paul; Mladen Pavicic

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We show that with an efficiency exceeding 99% one can use a monolithic total-internal-reflection resonator in order to ascertain the presence of an object without transferring a quantum of energy to it. We also propose an experiment on the probabilistic meaning of the electric field that contains only a very few photons.

Source: http://arxiv.org/abs/quant-ph/9908023v1

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Sep 21, 2013
09/13

by
Mladen Pavicic; Johann Summhammer

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We propose a new experiment employing two independent sources of spin correlated photon pairs. Two photons from different unpolarized sources each pass through a polarizer to a detector. Although their trajectories never mix or cross they exhibit 4th-order-interference-like correlations when the other two photons interfere on a beam splitter even when the latter two do not pass any polarizers at all. A wave packet calculation shows that the experiment permits a very discriminatory test of...

Source: http://arxiv.org/abs/1008.0078v2

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Sep 17, 2013
09/13

by
Norman D. Megill; Mladen Pavicic

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We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our...

Source: http://arxiv.org/abs/quant-ph/0108074v1

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Sep 22, 2013
09/13

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Mladen Pavicic; Norman D. Megill

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We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers. More specifically, we look for a way to feed a quantum computer with algebraic equations of n-th order underlying an infinite dimensional Hilbert space description of quantum systems. A number of new results on states defined on Hilbert lattices are presented...

Source: http://arxiv.org/abs/0812.3072v1

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Jul 19, 2013
07/13

by
Norman D. Megill; Mladen Pavicic

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Every set (finite or infinite) of quantum vectors (states) satisfies generalized orthoarguesian equations ($n$OA). We consider two 3-dim Kochen-Specker (KS) sets of vectors and show how each of them should be represented by means of a Hasse diagram---a lattice, an algebra of subspaces of a Hilbert space--that contains rays and planes determined by the vectors so as to satisfy $n$OA. That also shows why they cannot be represented by a special kind of Hasse diagram called a Greechie diagram, as...

Source: http://arxiv.org/abs/1005.0016v1

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Sep 22, 2013
09/13

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Norman D. Megill; Mladen Pavicic

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Quantum implication algebras without complementation are formulated with the same axioms for all five quantum implications. Previous formulations of orthoimplication, orthomodular implication, and quasi-implication algebras are analysed and put in perspective to each other and our results.

Source: http://arxiv.org/abs/quant-ph/0310062v1

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Jul 20, 2013
07/13

by
Norman D. Megill; Mladen Pavicic

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Several new results in the field of Hilbert lattice equations based on states defined on the lattice as well as novel techniques used to arrive at these results are presented. An open problem of Mayet concerning Hilbert lattice equations based on Hilbert-space-valued states is answered.

Source: http://arxiv.org/abs/quant-ph/0609192v2

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Jul 20, 2013
07/13

by
Norman D. Megill; Mladen Pavicic

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We provide several new results on quantum state space, on lattice of subspaces of an infinite dimensional Hilbert space, and on infinite dimensional Hilbert space equations as well as on connections between them. In particular we obtain an n-variable generalized orthoarguesian equation which holds in any infinite dimensional Hilbert space. Then we strengthen Godowski's result by showing that in an ortholattice on which strong states are defined Godowski's equations as well as the...

Source: http://arxiv.org/abs/quant-ph/0009038v3

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Jul 20, 2013
07/13

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Mladen Pavicic; Norman D. Megill

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It is shown that propositional calculuses of both quantum and classical logics are non-categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled by a weakly orthomodular lattice and that classical logic is in addition to a Boolean algebra also modeled by a weakly distributive lattice. Both new models turn out to be non-orthomodular. We prove the soundness and completeness of the calculuses for the models. We also prove that all the operations in an...

Source: http://arxiv.org/abs/quant-ph/9906101v3

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Sep 22, 2013
09/13

by
Norman D. Megill; Mladen Pavicic

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It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity of equivalence terms and several other 3 variable expressions involving equivalence terms have been proved to hold in any orthomodular lattice. Symmetric differences have been shown to reduce to complements of equivalence terms. Some congruence relations...

Source: http://arxiv.org/abs/quant-ph/0310063v1

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Sep 22, 2013
09/13

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Mladen Pavicic; Norman D. Megill

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It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and therefore cannot be distributive either - as opposed to the standard lattice models that are orthomodular and distributive for the respective logics. Hence, we cannot attribute the orthomodularity to quantum logic itself, and we cannot attribute the...

Source: http://arxiv.org/abs/0812.2698v1

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Sep 24, 2013
09/13

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Norman D. Megill; Mladen Pavicic

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We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is embeddable into the algebra. To obtain this result we devised algorithms and computer programs for obtaining expressions of all quantum and classical operations within an orthomodular lattice in terms of each other, many of which are presented in the paper. For...

Source: http://arxiv.org/abs/quant-ph/0103135v2

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Sep 22, 2013
09/13

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Mladen Pavicic; Norman D. Megill

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It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes, respectively. In this paper we prove that these logics are complete even for those classes of the former lattices from which the standard orthomodular lattices and Boolean algebras are excluded. We also show that neither quantum nor classical computers can be founded...

Source: http://arxiv.org/abs/0812.2702v1

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Sep 17, 2013
09/13

by
Norman D. Megill; Mladen Pavicic

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There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations. We obtain a result which opens a possibility that the first two classes coincide. We devise new algorithms to generate Mayet-Godowski equations that allow us to prove that the fourth class properly includes the third. An open problem related to the last class is answered....

Source: http://arxiv.org/abs/0912.1461v2

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Sep 23, 2013
09/13

by
Norman D. Megill; Mladen Pavicic

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The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct for any sample size.

Source: http://arxiv.org/abs/1105.1486v1

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Sep 19, 2013
09/13

by
Mladen Pavicic; Norman D. Megill; Jean-Pierre Merlet

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We show that all possible 388 4-dim Kochen-Specker (KS) (vector) sets (of yes-no questions) with 18 through 23 vectors and 844 sets with 24 vectors all with component values from \{-1,0,1\} can be obtained by stripping vectors off a single system provided by Peres 20 years ago. In addition to them, we have found a number of other KS sets with 22 through 24 vectors. We present the algorithms we used and features we found, such as, for instance, that Peres' 24-24 KS set has altogether six...

Source: http://arxiv.org/abs/0910.1311v4

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Jul 20, 2013
07/13

by
Brendan D. McKay; Norman D. Megill; Mladen Pavicic

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We give a new algorithm for generating Greechie diagrams with arbitrary chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer program for generating the diagrams. The results show that the previous algorithm does not produce every diagram and that it is at least 100,000 times slower. We also provide an algorithm and programs for checking of Greechie diagram passage by equations defining varieties of orthomodular lattices and give examples from Hilbert lattices. At the...

Source: http://arxiv.org/abs/quant-ph/0009039v3

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Sep 22, 2013
09/13

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Mladen Pavicic; Jean-Pierre Merlet; Brendan McKay; Norman D. Megill

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We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition...

Source: http://arxiv.org/abs/quant-ph/0409014v2

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Sep 22, 2013
09/13

by
Mladen Pavicic; Brendan D. McKay; Norman D. Megill; Kresimir Fresl

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Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices generated by McKay-Megill-Pavicic (MMP) hypergraphs and Hilbert subspace equations are given. To enable exhaustive generations of 3-dim KS setups by means of recently found "stripping technique," bipartite graph generation is used to provide us...

Source: http://arxiv.org/abs/1004.0776v2

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Sep 19, 2013
09/13

by
Mordecai Waegell; P. K. Aravind; Norman D. Megill; Mladen Pavicic

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The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a...

Source: http://arxiv.org/abs/1010.4353v3

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Sep 22, 2013
09/13

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Mladen Pavicic; Norman D. Megill; P. K. Aravind; Mordecai Waegell

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We find a new highly symmetrical and very numerous class (millions of non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the nature of their geometrical symmetries, they cannot be obtained from previously known ones. We generate the sets from a single set of 60 orthogonal spin vectors and 75 of their tetrads (which we obtained from the 600-cell) by means of our newly developed "stripping technique." We also consider "critical KS subsets" and analyze their...

Source: http://arxiv.org/abs/1004.1433v2

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Sep 23, 2013
09/13

by
Norman D. Megill; Kresimir Fresl; Mordecai Waegell; P. K. Aravind; Mladen Pavicic

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We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these sets, and it gives all sets while the parity proof method gives only sets with an odd number of edges in their hypergraph representation. Thus we obtain 35 new kinds of critical KS sets with an even number of edges. Using a random sample of the sets generated...

Source: http://arxiv.org/abs/1105.1840v1