Probabilistic Logics in Quantum Computation

Freytes, Héctor; Ledda, Antonio; Sergioli, Giuseppe; Giuntini, Roberto

doi:10.1007/978-94-007-5845-2_5

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Fuzzy-like structures have appeared in this context which have been extensively studied [12,13,18]. However, as noted in [16], this fuzzy behavior is mainly due to probabilistic features concerning uncertainty aspects of a state. Namely, the probabilities of a state to be detected either in the "false" state P (2 n ) 0 , or in the "true" state P (2 n ) 1…”

Section: Degrees Of Truthmentioning

confidence: 99%

A note on many valued quantum computational logics

Sergioli

Ledda

2015

Soft Comput

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The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space C 3 , we discuss extensions of several gates to this space and, using the notion of effect probability, we provide a characterization of its states.

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Section: Degrees Of Truthmentioning

confidence: 99%

A note on many valued quantum computational logics

Sergioli

Ledda

2015

Soft Comput

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“…The theory of quantum computation has suggested new forms of quantum logic -the so called quantum computational logics -that turn out to have some typical unsharp features [4]. The main difference between the quantum logic introduced by Birkhoff and von Neumann [3] and the quantum computational logics, could be summarized as follows: in the Birkhoff and von Neumann approach, the meaning of a sentence is interpreted as a closed subspace of the Hilbert space associated with a physical system [5]; on the other hand, in quantum computational logics the meaning of a sentence is identified with a quantum information quantity: a qubit, a quregister (that is a system of qubits) or, more generally, a mixture of quregisters (the so called qumix ) [6,7,8,11,14].…”

Section: Introductionmentioning

confidence: 99%

Binary Gates in Three Valued Quantum Computational Logics

Sergioli¹,

Ledda²,

Giuntini³

2016

Probing the Meaning of Quantum Mechanics

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The standard theory of quantum computation relies on the idea that the qubit-the basic information quantity-is represented by a superposition of elements of the standard quantum computational basis B (2) = {|0 , |1 }. In the present paper we focus on the case of qutrits where the standard quantum computational bases is replaced by a three-valued computational basis B (3) = {|0 , | 1 2 , |1 }. Recently in [13], unary gates on the Hilbert space C 3 were considered. In this work we propose an extensive method that allows to extend binary gates to the framework of qutrits.

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Against the Tyranny of ‘Pure States’ in Quantum Theory

Ronde

Massri

2021

Found Sci

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In this paper we provide arguments against the dominant role played by the notion of pure sate within the orthodox account of quantum theory. Firstly, we will argue that the origin of this notion is intrinsically related to the widespread empirical-positivist understanding of physics according to which 'theories describe actual observations of subjects (or agents)'. Secondly, we will show how within the notion of pure state there is a scrambling of two mutually incompatible definitions. On the one hand, a contextual definition which attempts to provide an intuitive physical grasp in terms of the certain prediction of a measurement outcome; and on the other hand, a noncontextual purely abstract mathematical definition which has no clear physical content. We will then turn our attention to the way in which pure states and mixtures have been considered by two categorical approaches to QM, namely, the topos approach originally presented by Chris Isham and Jeremy Butterfield [27, 28, 29] and the more recent logos categorical approach presented by the authors of this article [11, 12]. While the first approach presents serious difficulties in order to produce an orthodox understanding of pure states and mixtures, the latter presents a new scheme in which the distinction between pure states and mixtures becomes completely irrelevant.

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Probabilistic Logics in Quantum Computation

Cited by 3 publications

References 17 publications

A note on many valued quantum computational logics

A note on many valued quantum computational logics

Binary Gates in Three Valued Quantum Computational Logics

Against the Tyranny of ‘Pure States’ in Quantum Theory

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