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arXiv:2412.04397

Multi-Screen Entanglement in Tensorial Quantum Mechanics

Christian DE RONDE, Raimundo Fernández Mouján, César Massri

Published Dec 5, 2024• 0 citations
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Abstract

In this work we present an invariant-objective formalization of multi screen-entanglement grounded on Tensorial Quantum Mechanics (TQM) [12]. This new tensorial formulation of the theory of quanta -- basically, an extension of Heisenberg's matrix mechanics -- allows not only to escape the many problems present in the current account of multi-partite entanglement grounded on the Dirac-Von Neumann Standard formulation of Quantum Mechanics (SQM) but, more importantly, to consistently represent entanglement phenomena when considering a multiplicity of different screens and detectors.

DOI
10.48550/arxiv.2412.04397

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In this work we present an invariant-objective formalization of multi screen-entanglement grounded on Tensorial Quantum Mechanics (TQM) [12]. This new tensorial formulation of the theory of quanta -- basically, an extension of Heisenberg's matrix mechanics -- allows not only to escape the many problems present in the current account of multi-partite entanglement grounded on the Dirac-Von Neumann Standard formulation of Quantum Mechanics (SQM) but, more importantly, to consistently represent entanglement phenomena when considering a multiplicity of different screens and detectors.
In July 1925, exactly one century ago, Werner Heisenberg created Quantum Mechanics (QM) as an invariant-operational formalism by taking as a standpoint the intensive patterns that had been already observed by experimentalists in the lab. One of the few drawbacks of this proposal was the impossibility to conceptualize it in classical terms. Attempting to restore a somewhat classical spatiotemporal representation, six months later, Erwin Schrödinger would present a formalism grounded on a wave equation in configuration space. Taking as a standpoint Schrödinger’s wave mechanics together with the methodological guide of Bohr and logical positivists, Dirac would present in 1930 an axiomatic re-formulation of the theory of quanta that would become known as the “standard” version of QM (SQM). This new version of the theory, that is still today taught in physics classrooms all around the world, would become accepted regardless of its inconsistent narrative as a “recipe” intended (but unable) to predict (binary) measurement outcomes. After pointing out some of the many problems of SQM, in this work we propose to go back to Heisenberg’s matrix mechanics (and also to his understanding of physical theories). We will argue that his matrix mechanics, as an operationally-invariant standpoint, opens the door to a tensorial enlargement of the mathematical formalism capable to account for new phenomena.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents unique challenges and opportunities for information processing. This paper proposes a novel tensor analysis framework predicated on quantum entanglement, incorporating specific tensor operations designed to precisely capture the intricacies of this correlation. The core claim is that this framework enables more efficient and robust quantum computation through the strategic application of entanglement-based computations and a newly designed tensor operation. The mechanism involves leveraging quantum entanglement to store and manipulate information, offering a potential paradigm shift in quantum information processing. This work explores the theoretical foundations and potential implementation of this approach, demonstrating its capacity to address limitations of traditional tensor analysis methods.
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive representation of quantum states for multiple qubits and the quantum gates that manipulate them. The proposed formalism could contribute to a more intuitive representation of qubit states, and to a clear visualisation of the entanglement property. The main advantages of this formalism are that it preserves the fundamental structure of the Hilbert space to which quantum states belong, and also reduces the computational cost associated with classical prediction of the effect of quantum gates on multi-qubit states. A connection between the ability to generate entanglement and the quantum gate representation is also established.
In this work we discuss the establishment of Standard Quantum Mechanics (SQM) developed through Schrödinger's and Dirac's wave-vectorial reformulations of Heisenberg's original matrix mechanics. We will argue that while Heisenberg's approach was consistently developed -- taking as a standpoint the intensive patterns that were observed in the lab -- as an invariant-operational formalism, Dirac's axiomatic re-formulation was, instead, developed -- taking as a standpoint Schrödinger's wave mechanics and the methodological guide of Bohr and logical positivists -- as an essentially inconsistent "recipe" intended (but unable) to predict (binary) measurement outcomes. Leaving SQM behind and attempting to restore the consistent and coherent account of a real state of affairs, we will present a new tensorial proposal which -- taking as a standpoint Heisenberg's original approach -- will prove capable not only to extend the matrix formalism to a tensorial representation but also to account for new experimental phenomena.
Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.
Quantum entanglement, a cornerstone of quantum mechanics, presents unique challenges to traditional modeling approaches. The non-locality inherent in entangled states complicates fundamental understanding and control. This paper proposes a novel framework, leveraging tensor categories, to address this challenge, aiming to model and manipulate entanglement with enhanced precision. We construct a model that dynamically adjusts entangled states, utilizing tensor categories to encapsulate the non-locality inherent in the system. This approach offers a more intuitive and controllable way to operate on quantum information, potentially unlocking new computational capabilities. The core claim is that this framework provides a fundamental shift in our understanding and manipulation of entangled states, enabling novel quantum algorithms and information processing techniques. The work explores the potential of tensor categories to represent and manipulate entanglement, leading to a more robust and insightful model of quantum phenomena.