Quantum Mechanics And Quantum Information.Physical, Philosophical And Logical Approaches.

Brussels Free University, Belgium, 23 and 24 of July 2015

Book of Abstracts

Vrije Universiteit Brussel, Belgium

Center Leo Apostel Brussels, Belgium

Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina

Universidad Nacional Arturo Jauretche, Argentina

Università degli Studi di Cagliari, Italy

Acknowledgements

This meeting was made possible by the following institutions, whose financial support is gratefullyacknowledged:

- FWO project G.0405.08 and FWO-research community W0.030.06.- CONICET RES. 4541-12 (11/01/2014 al 11/01/2015).- Ministero Italiano per l’Università e la Ricerca within the FIRB project, “Structures andDynamics of Knowledge and Cognition”, project number RBFR126ZA6_005.

- Regione Autonoma della Sardegna, within the project “Le strutture Computazionali Quan-tistiche a servizio del Pattern Recognition: modellare l’incertezza”, project number F71J12001020002,L.R. 7/2007, CRP-59872.

Scientific Committee

Newton da Costa (Federal University of Santa Catarina)Diederik Aerts (Leo Apostel Centre - CLEA; Brussels Free University - VUB )Maria Luisa Dalla Chiara (University of Florence)Roberto Giuntini (University of Cagliari)Décio Krause (Federal University of Santa Catarina )

Organizing Committee

Christian de Ronde (Inst. de Filosofia Dr. Alejandro Korn, UBA-CONICET) – ChairHector Freytes (University of Cagliari, UNR-CONICET)Antonio Ledda (University of Cagliari)Giuseppe Sergioli (University of Cagliari)

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List of Participants

- Bob Coecke- Marisa Dalla Chiara- Christian de Ronde- Benjamin Eva- Hector Freytes- Matias Graffigna- Roberto Giuntini

- Antonio Ledda

- Roberto Leporini

- Giuseppe Sergioli

- Albert Solé

- Tomas Veloz

- Karin Verelst

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Index of Abstracts

From quantum foundations to natural language meaning via string diagramsBob Coecke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Quantum Turing Machines, Quantum Computational Logic and Cognitive ProcessesMaria Luisa Dalla Chiara, Roberto Giuntini, Giuseppe Sergioli, Roberto Leporini . . . 1

Quantum Superpositions Do Exist! But Quantum Reality 6= ActualityChristian de Ronde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Another Paraconsistent Topos Theoretic Quantum LogicBenjamin Eva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Non-separability in Quantum Computation: representing continuous t-normHector Freytes, Giuseppe Sergioli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

From sharp to unsharp quantum logic:A new look at the effects of a Hilbert space (1)Roberto Giuntini, Antonio Ledda, Francesco Paoli . . . . . . . . . . . . . . . . . . . . 3

From sharp to unsharp quantum logic:A new look at the effects of a Hilbert space (2)Roberto Giuntini, Antonio Ledda, Francesco Paoli . . . . . . . . . . . . . . . . . . . . 4

The possibility of a new metaphysics for quantum mechanics from the phenomeno-logical perspective: Meinong and HusserlMatias Graffigna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Quantum Pattern RecognitionGiuseppe Sergioli, Roberto Giuntini . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

A defence of the two-space reading of Bohmian mechanicsAlbert Solé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

On new interpretational aspects on the quantum-inspired approach to cognitionTomas Veloz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Structure as CauseKarin Verelst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

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From quantum foundations to natural language meaning via stringdiagrams

Bob CoeckeOxford University

Earlier work on an entirely diagrammatic formulation of quantum theory, which is soon toappear in the form of a textbook [1], has somewhat surprisingly guided us towards providingan answer for the following question: how do we produce the meaning of a sentence giventhat we understand the meaning of its words? The correspondence between these seem-ingly far apart areas was established in terms of string diagrams [2, 3], and more recently,also internal Frobenius algebras and completely positive maps have started to play a keyrole in both areas. This work has practical applications in the area of Natural LanguageProcessing. The fact that meaning in natural language, depending on the subject domain,encompasses discussions within any scientific discipline, we obtain a template for theoriessuch as animal behaviour, social interaction, and many others.

Bibliography

1 B. Coecke and A. Kissinger (2014) Picturing Quantum Processes. Cambridge UP.2 B. Coecke, M. Sadrzadeh and S. Clark (2010) Mathematical foundations for a com-

positional distributional model of meaning. Linguistic Analysis - Lambek festschrift.arXiv:1003.4394

3 B. Coecke (2012) The logic of quantum mechanics - Take II. arXiv:1204.3458

Quantum Turing Machines, Quantum Computational Logic andCognitive Processes

Maria Luisa Dalla Chiara1 Roberto Giuntini2Giuseppe Sergioli2 Roberto Leporini3

1University of Florence2University of Cagliari3University of Bergamo

Parallelism represents an essential aspect of human mind/brain activities. One can recog-nize some common features between psychological parallelism and the characteristic parallelstructures that arise in quantum theory and in quantum computation. The talk is devotedto a discussion of the following questions: 1. a comparison between classical probabilisticTuring machines and quantum Turing machines. 2. Possible applications of the quantumcomputational semantics to cognitive problems.

Bibliography

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1 M.L. Dalla Chiara, H. Freytes, R. Giuntini, A. Ledda, R. Leporini, G. Sergioli, “En-tanglement as a semantic resource”, Foundations of Physics 40, pp. 1494-1518, 2011.

2 E. Beltrametti, M.L. Dalla Chiara, R. Giuntini, G. Sergioli, “Quantum teleportationand quantum epistemic semantics”, Mathematica Slovaca 62, pp. 1-24, 2012.

3 M.L. Dalla Chiara, R. Giuntini, R. Leporini, G. Sergioli, “Holistic logical argumentsin quantum computation”, to appear in Mathematica Slovaca.

4 M.L. Dalla Chiara, R. Giuntini, A.R. Luciani, E. Negri, “From Quantum Informationto Musical Semantics”, illustrated by C. Seravalli, College Publications, London, 2012.

Quantum Superpositions Do Exist! But Quantum Reality 6=Actuality

Christian de RondeCenter Leo Apostel, University of Buenos Aires/CONICET

In this presentation we analyze the definition of quantum superpositions within orthodoxQuantum Mechanics (QM) and their relation to physical reality. We will begin by discussinghow the metaphysical presuppositions imposed by Bohr on the interpretation of QM havebecome not only interpretational dogmas which constrain the limits of the present OrthodoxLine of Research (OLR), but also how these desiderata implicitly preclude the possibilityof developing a physical representation of quantum superpositions. We will then continueanalyzing how most interpretations of QM argue against the existence of superpositions.Firstly, we will focus on those interpretations which attempt to recover a classical represen-tation about “what there is”, and secondly, we will concentrate on the arguments providedby Dieks and Griffiths who, staying close to the orthodox formalism, also attempt to “getrid of the ghost of Schrödinger’s cat”. Contrary to the OLR, we will argue —based on ourdefinition of Meaningful Physical Statements (MPS)— that from a representational realistperspective which stays close to the orthodox Hilbert space formalism, quantum superpo-sitions are not only the key to the most important —present and future— technologicaland experimental developments in quantum information processing but also, they must beconsidered as the kernel of any interpretation of QM that attempts to provide a physicalrepresentation of reality. We will also argue that the price to pay for such representationalrealist development must be the abandonment of the (dogmatic) idea that ‘Actuality =Reality’.

Another Paraconsistent Topos Theoretic Quantum Logic

Benjamin EvaUniversity of Bristol

In this talk, I will describe a new paraconsistent logical structure that arises naturally in thecontext of tops quantum theory (of the kind developed by Isham, Doering etc). Specifically,

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I will show how the natural tops theoretic ‘translation’ of the orthocomplement operationfamiliar from traditional orthomodular quantum logic gives rise to a new paraconsistentnegation that models a particular kind of relevance logic. Finally, I will show how this newparaconsistent structure allows for the development of a connection between topos quantumtheory and quantum set theory (of the type studies by Takeuti, Ozawa, Titani etc).

Non-separability in Quantum Computation: representingcontinuous t-norm

Hector Freytes Giuseppe SergioliUniversity of Cagliari

In order to establish a connection between quantum computation with mixed states andfuzzy logic of continuous t-norms, we provide a representation of the Łukasiewicz t-normin terms of special kinds of quantum operations (called “polynomial quantum operations”).Using non-factorized quantum states, we show an efficient strategy to improve this repre-sentation and we introduce the set of Werner states as an interesting example.

From sharp to unsharp quantum logic:A new look at the effects of a Hilbert space (1)

Roberto Giuntini Antonio Ledda Francesco PaoliUniversity of Cagliari

The starting point of the unsharp approach to quantum mechanics (QM) ([2]) is deeplyconnected with a general problem that naturally arises in the framework of Hilbert spacequantum theory. Let us consider an event-state system (Π(H) ,S(H)), where Π(H) is the setof projections, while S(H) is the set of all density operators of the Hilbert spaceH (asso-ciated to the physical system under investigation). Do the sets Π(H) and S(H) correspondto an optimal possible choice of adequate mathematical representatives for the intuitive no-tions of event and of state, respectively? Once Π(H) is fixed, Gleason’s Theorem guaranteesthat S(H) corresponds to an optimal notion of state: for, any probability measure definedon Π(H) is determined by a density operator of H (provided the dimension of H is greaterthan or equal to 3). On the contrary, Π(H) does not represent the largest set of operatorsassigned a probability-value since there are bounded linear operators E of H that are notprojections and that satisfy the Born’s rule: for any density operator ρ, Tr(ρE) ∈ [0, 1].In the unsharp approach to QM, the notion of quantum event is liberalized and the setΠ(H) is replaced by the set of all effects of H (denoted by E(H)), where an effect of H is abounded linear operator E that satisfies the following condition, for any density operatorρ : Tr(ρE) ∈ [0, 1]. Clearly, E(H) properly includes Π(H).

The set E(H) can be naturally structured ([1],[2]) as a Brouwer-Zadeh poset (BZ-poset)〈E(H) , ≤ , ′ , ∼ ,O , I〉, where(i) E ≤ F iff for any density operator ρ ∈ S(H) : Tr(ρE) ≤ Tr(ρF );

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(ii) E′ = I− E (where − is the standard operator difference);

(iii) E∼ = PKer(E), where PKer(E) is the projection associated to the kernel of E;

(iv) O and I are the null and the identity projections, respectively.

The BZ-poset E(H) turns out to be properly fuzzy since the noncontradiction principleis violated (E ∧ E′ 6= O). Further, the BZ-poset E(H) fails to be a lattice ([2]). In a quiteneglected paper, however, Olson ([4]) proved that E(H) can be equipped with a naturalpartial order ≤s (called spectral order) in such a way that 〈E(H),≤s〉 turns out to be acomplete lattice.

Bibliography

[1] G. Cattaneo and G. Nisticò, “Brouwer-Zadeh posets and three-valued Ł posets”, Fuzzy Setsand Systems 33, 165–190, 1986.

[2] M. L. Dalla Chiara, R. Giuntini and R. Greechie, Reasoning in Quantum Theory, Kluwer,Dordrecht, 2004.

[3] H. F. de Groote, “On a canonical lattice structure on the effect algebra of a von Neumannalgebra”, arXiv:math-ph/0410018v2, 2005.

[4] M. P. Olson, “The selfadjoint operators of a von Neumann algebra form a conditionally com-plete lattice”, Proceedings of the American Mathematical Society 28, 537–544, 1971.

From sharp to unsharp quantum logic:A new look at the effects of a Hilbert space (2)

Roberto Giuntini Antonio Ledda Francesco PaoliUniversity of Cagliari

In this second part, we discuss the algebraic properties of the structure 〈E(H) , ≤s ,′ , ∼ ,O , I〉

and we will introduce a new class of paraorthomodular Brower Zadeh lattices (calledPBZ∗ − lattices) that represents a quite faithful abstraction of the concrete model basedon E(H). Interestingly enough, in the framework of PBZ∗-lattices different abstract notionsof “unsharpness” collapse into the one and the same concept, similarly to what happens inthe concrete BZ∗-lattices of all effects. We will show that no nontrivial lattice identity issatisfied byPBZL∗ and that the equational theory of Kleene lattices is conservatively ex-tended by the equational theory of BZ lattices. In particular, we prove that every boundedlattice can be embedded as a sublattice into a PBZ∗-lattice. Furthermore, we start theinvestigation of the lattice of subvarieties of PBZL∗. This enterprise is likely to be a trickyone: after all, not much is known even about varieties of orthomodular lattices.

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The possibility of a new metaphysics for quantum mechanics fromthe phenomenological perspective: Meinong and Husserl

Matias GraffignaUniversity of Buenos Aires

According to de Ronde it was Bohr’s interpretation of quantum mechanics (QM) whichclosed the possibility of understanding physical reality beyond the realm of the actual, soestablishing the Orthodox Line of Research. In this sense, it is not the task of any physicaltheory to look beyond the language and metaphysics supposed by classical physics, in orderto account for what QM describes. If one wishes to maintain a realist position (though notnaive) regarding physical theories, one seems then to be trapped by an array of conceptsthat do not allow to understand the main principles involved in the most successful physicaltheory thus far, mainly: the quantum postulate, the principle of indetermination and thesuperposition principle. If de Ronde is right in proposing QM can only be completed as aphysical theory by the introduction of “new concepts” that admit as real a domain beyondactuality, then a new ontology that goes beyond Aristotelian and Newtonian actualism isneeded. It was already in the early 20th century that misunderstood philosopher Alexiusvon Meinong proposed a Theory of Objects that admits a domain of being beyond existence-actuality. Member of the so called “School of Brentano”, Meinong’s concerns were orientedto provide an ontology of everything that can be thought of, and at the same time anintentionality theory of how objects are thought of. I wish to argue that in Meinong’stheory of objects we find the rudiments of the ontology and the intentionality theory weneed to account for QM’s basic principles: mainly the possibility of predicating propertiesof non-entities, or in other words, the possibility of objectively describing a domain of whatis, that is different from the domain of actual existence; in de Ronde’s words: powers withdefinite potentia.

Quantum Pattern Recognition

Giuseppe Sergioli Roberto GiuntiniUniversity of Cagliari

Apparently, Quantum Computation and Pattern Recognition are two different topics witha strong common point: the uncertainty plays a relevant role in both fields. We proposeto formalize all the theoretical framework of Pattern Recognition in term of Quantumobjects. In particular, uncertain patterns are represented by quantum mixed states andthe classification process is made by introducing an "ad hoc" normalization of the TraceDistance. Some open questions are introduced at the end.

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A defence of the two-space reading of Bohmian mechanics

Albert SoléAutonomous University of Barcelona

In this talk I compare two quantum ontologies, wave function field monism and the two-space reading of Bohmian mechanics, defending the latter from certain recent criticisms inthe literature. Wave function field monism is the view that the wave function –interpretedas a physical field inhabiting the 3N-dimensional configuration space– is all that there fun-damentally is. Authors such as David Albert or Alyssa Ney consider that realism aboutordinary non- relativistic quantum mechanics commits to this view. Bohmian mechanics isa theory of point particles whose trajectories depend on the wave function. According tothe two-space reading of Bohmian mechanics both the wave function and the particles exist.The wave function is interpreted as a physical field in configuration space while the particlesare taken to inhabit the ordinary three-dimensional space. Therefore, this view is commit-ted to the physical existence of both configuration space and ordinary three-dimensionalspace. The first criticism of the two- space reading of Bohmian mechanics that I will con-sider is due to Ney [1]. In brief, Ney argues that if the two space reading of Bohmianmechanics is true, the Bohmian particles are causally inert. Since it is assumed that macro-scopic objects are constituted by Bohmian particles, macroscopic objects are causally inertas well. Therefore, Ney concludes the friend of the two-space reading of Bohmian mechan-ics is forced to a notorious revision of the manifest image regarding the causal propertiesthat we typically attribute to the objects of our experience. Here, I will argue, first, thatit is not a consequence of the two-space reading of Bohmian mechanics that the Bohmianparticles are causally inert. However, I agree with Ney in that the friend of the two-spacereading of Bohmian mechanics is forced to a certain revision of the causal properties that wetypically attribute to macro-objects. Second, I will provide some plausibility arguments tothe conclusion that the wave function field monist that endorses Ney’s account of reduction[1] has also to revise some beliefs about causation that are part of the manifest image. Iftime allows, I will consider a second objection against the two-space reading of Bohmianmechanics raised by advocates of the Everett interpretation. These latter notice that thefriend of the two-space reading of Bohmian mechanics includes the wave function in herontology, exactly as Everettians do. Since the existence of the wave function is enough toground the existence of many worlds, it turns out that the Bohmian has to accept manyworlds in her ontology and that the Bohmian particles are idle ontological posits. Here Iwill argue that the friend of the two-space reading of Bohmian mechanics has conceptualresources to counteract this latter argument as well.

Bibliography

1 Ney, A. (2012): The Status of our Ordinary Three Dimensions in a Quantum Universe.Nous 46(3), 525–560.

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On new interpretational aspects on the quantum-inspiredapproach to cognition

Tomas VelozUniversity of British Columbia

The quantum approach to cognition has become increasingly influential on areas such aspsychology, economics, and information retrieval. In particular the mathematical structuresfound in quantum mechanics have shown to provide an interesting modeling framework fora number of cognitive problems of seemingly different nature. Some new experimentalresults have provided strong evidence that the quantum cognition is not only a suitablemathematical framework for cognitive phenomena. Also, it provides a sensible definition forsome notions that are ‘as relevant as not well understood in cognition’, such as emergence,modes of thought, distinguishability, and coherence. We present these new experimentalevidence, and elaborate on the above mentioned notions with the aim to characterize aradically new approach to cognitive phenomena.

Structure as Cause

Karin VerelstVrije Universiteit Brussel

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