Physics papers by Mladen Pavičić
We show that all possible 388 4-dim Kochen–Specker (KS)(vector) sets (of yes–no questions) with 1... more 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 critical KS subsets.
Abstract We give a constructive and exhaustive definition of Kochen–Specker (KS) vectors in a Hil... more Abstract 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, ie, vectors in an n-dimensional Hilbert space, Hn, 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.
Papers by Mladen Pavičić
arXiv (Cornell University), Feb 16, 2022
Development of quantum computation and communication, recently shown to be supported by contextua... more Development of quantum computation and communication, recently shown to be supported by contextuality, arguably asks for a requisite supply of contextual sets. While that has been achieved in even dimensional spaces, in odd dimensional spaces only a dozen contextual critical Kochen-Specker (KS) sets have been found so far. In this paper we give three methods for automated generation of arbitrarily many contextual KS and non-KS sets in any dimension for possible future application and implementation and we employ them to obtain millions of KS and other contextual sets in dimensions 3, 5, 7, and 9 where previously only a handful of sets have been found. Also, no explicit vectors for the original Kochen-Specker set were known so far, while we now generate them from 24 vector components.
Zbirka se sastoji od 218 zadataka od kojih je polovica detaljno rijesena ali tako da je diferenci... more Zbirka se sastoji od 218 zadataka od kojih je polovica detaljno rijesena ali tako da je diferencijalni i integralni racun rađen pomocu limesa i suma. Zadaci su podijeljeni prema nastavnim jedinicima ; 1. Mehanika ; 2. Toplina i molekularna fizika ; 3. Optika ; 4. Elektricitet. Na kraju su dane tabele jedinica te literatura. Kompletni udzbenik je skeniran 2015.g. i dan kao pdf file na dolje navedenim linkovima.
The simplest possible photon-number-squeezed states containing only two photons and exhibiting su... more The simplest possible photon-number-squeezed states containing only two photons and exhibiting sub-poissonian statistics with the Fano factor approaching 0.5 have been used for a proposal of a loophole-free Bell experiment requiring only 67 percent of detection efficiency. The states are obtained by the fourth order interference first of two downconverted photons at an asymmetrical beam splitter and thereupon of two photons from two independent singlets at an asymmetrical beam splitter. In the latter set-up, the other two photons which nowhere interacted and whose paths never crossed appear entangled in a singlet-like correlated state.
arXiv (Cornell University), May 14, 2023
Recently, handling of contextual sets, in particular Kochen-Specker (KS) sets, in higher dimensio... more Recently, handling of contextual sets, in particular Kochen-Specker (KS) sets, in higher dimensions has been given an increasing attention, both theoretically and experimentally. However, methods of their generation are diverse, not generally applicable in every dimension, and of exponential complexity. Therefore, we design a dimensional upscaling method, whose complexity does not scale with dimension. As a proof of principle we generate manageable-sized KS master sets in up to 27 dimensional spaces and show that well over 32 dimensions can be reached. From these master sets we obtain an ample number of smaller KS sets. We discuss three kinds of applications that work with KS sets in higher dimensions. We anticipate other applications of KS sets for quantum information processing that make use of large families of nonisomorphic KS sets.
We give a new algorithm for generating Greechie diagrams with arbitrary chosen number of atoms or... more 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 10 5 times slower. We also provide an algorithm and programs for checking Greechie diagram passage by equations defining varieties of orthomodular lattices and give examples from Hilbert lattices. We also discuss some additional characteristics of Greechie diagrams.
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and ... more 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 quantum disjunction and conjunction we prove their associativity in an orthomodular lattice for any triple in which one of the elements commutes with the other two and their distributivity for any triple in which a particular element commutes with the other two. We also prove that the distributivity of symmetric identity holds in Hilbert space, although whether or not it holds in all orthomodular lattices remains an open problem, as it does not fail in any of over 50 million Greechie diagrams we tested.
Proceedings of SPIE, Jul 13, 2000
Recently we proved that there are two non-isomorphic models of the calculus of quantum logic corr... more Recently we proved that there are two non-isomorphic models of the calculus of quantum logic corresponding to an infinite-dimensional Hilbert space representation: an orthomodular lattice and a weakly orthomodular lattice. We also discovered that there are two non-isomorphic models of the calculus of classical logic: a distributive lattice (Boolean algebra) and a weakly distributive lattice. In this work we consider implications of these results to a quantum simulator which should mimic quantum systems by giving precise instructions on how to produce input state, how to evolve them, and how to read off the final states. We analyze which conditions quantum states of a quantum computer currently obey and which they should obey in order to enable full quantum computing, i.e., proper quantum mathematics. In particular we find several new conditions which lattices of Hilbert space subspaces must satisfy.
Nanoscale Research Letters, Jul 18, 2019
The editors have retracted this article [1] because after publication concerns were raised regard... more The editors have retracted this article [1] because after publication concerns were raised regarding the validity of the conclusions drawn. Post-publication peer review has revealed a flaw in the application of the key rate equation r = IAB-IAE. For calculation of the term IAE, the effect of disturbance (D) on both the message mode (MM) and control mode (CM) was not taken into account. The main claim of the paper cannot be reliably reached. The author does not agree to this retraction.
Physics Letters, Feb 1, 2016
We present a scheme of deterministic mediated superdense coding of entangled photon states employ... more We present a scheme of deterministic mediated superdense coding of entangled photon states employing only linear-optics elements. Ideally, we are able to deterministically transfer four messages by manipulating just one of the photons. Two degrees of freedom, polarization and spatial, are used. A new kind of source of heralded down-converted photon pairs conditioned on detection of another pair with an efficiency of 92% is proposed. Realistic probabilistic experimental verification of the scheme with such a source of preselected pairs is feasible with today's technology. We obtain the channel capacity of 1.78 bits for a full-fledged implementation.
International Journal of Quantum Information, Oct 1, 2011
We discuss a scheme for a full superdense coding of entangled photon states employing only linear... more 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 discarding 33% of incoming photons.
Annales Henri Poincaré, Jan 13, 2010
There are five known classes of lattice equations that hold in every infinite dimensional Hilbert... more There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet's EA, 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. Finally, we show some new results on the Godowski lattices characterising the third class of equations.
Reports on Mathematical Physics, Dec 1, 2009
We propose a kind of reverse Kochen-Specker theorem that amounts to generating orthomodular latti... more 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 our notation.
Physics Letters, Jun 1, 1987
The eigenvalue equations for the complex Pauli unique gaussians as well as for the non-unique one... more The eigenvalue equations for the complex Pauli unique gaussians as well as for the non-unique ones are given, and the general solutions to them are outlined. In addition, it is proved that not all real states are Pauli unique. Recently, complex gaussians have been exploited as basis functions for a description of molecular motions which include vibrations in the semiclassical approach [1], for a comparison ofquantum and classical mechanics [2], with electronic structure investigations [3], etc. The gaussians were in general given [1] by wk=Cexp[-ak(q-qo)+ipo
International Journal of Theoretical Physics, Dec 1, 2003
It is shown that operations of equivalence cannot serve for building algebras which would induce ... more 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 related to equivalence operations and symmetric differences have been considered.
arXiv (Cornell University), Jun 27, 1999
It is shown that propositional calculuses of both quantum and classical logics are noncategorical... more It is shown that propositional calculuses of both quantum and classical logics are noncategorical. 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 orthomodular lattice are five-fold defined. In the end we discuss possible repercussions of our results to quantum computations and quantum computers.
Nucleation and Atmospheric Aerosols, 2004
Algorithms for finding arbitrary sets of Kochen-Specker (KS) qunits (n-level systems) as well as ... more 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 0-1 states or not. The complexity of the algorithms is polynomial. New results obtained with the help of the algorithms are presented.
Uploads
Physics papers by Mladen Pavičić
Papers by Mladen Pavičić