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26 pages, 345 KiB

Open AccessArticle

Towards Two Bloch Sphere Representation of Pure Two-Qubit States and Unitaries

by Stanislav Filatov and Marcis Auzinsh

Entropy 2024, 26(4), 280; https://0-doi-org.brum.beds.ac.uk/10.3390/e26040280 - 25 Mar 2024

Viewed by 693

We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative [...] Read more.

We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative direction of the coordinate axes of the two Bloch spheres may be used to describe the states. Moreover, the coordinate axes of one Bloch sphere should be rignt-handed and those of the other one should be left-handed. We describe and depict separable and maximally entangled states as well as entangling and non-entangling rotations. We also offer a graphical representation of the workings of a CNOT gate for different inputs. Finally, we provide a way to also represent partially entangled states and describe entanglement measures related to the surface area of the sphere enclosing the state representation. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

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8 pages, 218 KiB

Open AccessArticle

(Re)Construction of Quantum Space-Time: Transcribing Hilbert into Configuration Space

by Karl Svozil

Entropy 2024, 26(3), 267; https://0-doi-org.brum.beds.ac.uk/10.3390/e26030267 - 18 Mar 2024

Viewed by 642

Abstract

Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. [...] Read more.

Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

24 pages, 684 KiB

Open AccessArticle

Quantum State Reduction of General Initial States through Spontaneous Unitarity Violation

by Aritro Mukherjee, Srinivas Gotur, Jelle Aalberts, Rosa van den Ende, Lotte Mertens and Jasper van Wezel

Entropy 2024, 26(2), 131; https://0-doi-org.brum.beds.ac.uk/10.3390/e26020131 - 31 Jan 2024

Cited by 2 | Viewed by 701

Abstract

The inability of Schrödinger’s unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the [...] Read more.

The inability of Schrödinger’s unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the thermodynamic limit. Here, we introduce a family of models for spontaneous unitarity violation that apply to generic initial superpositions over arbitrarily many states, using either single or multiple state-independent stochastic components. Crucially, we show that Born’s probability rule emerges spontaneously in all cases. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

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9 pages, 285 KiB

Open AccessArticle

How Quantum Mechanics Requires Non-Additive Measures

by Gabriele Carcassi and Christine A. Aidala

Entropy 2023, 25(12), 1670; https://0-doi-org.brum.beds.ac.uk/10.3390/e25121670 - 18 Dec 2023

Viewed by 1125

Abstract

Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and, therefore, we set ourselves to construct the [...] Read more.

Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and, therefore, we set ourselves to construct the quantum equivalent of the Liouville measure. Unlike the classical counterpart, this quantized measure is non-additive and has a unitary lower bound (i.e., no set of states can have less than one state). Conversely, requiring that state quantification is finite for finite continuous regions and that each state counts as one already implies non-additivity, which in turn implies the failure of classical theory. In this article we show these preliminary results and outline a new line of inquiry that may provide a different insight into the foundations of quantum theory. Additionally, this new approach may prove to be useful to those interested in a quantized theory of space-time, as we believe this requires a quantized measure for the quantification of the independent degrees of freedom. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

26 pages, 381 KiB

Open AccessFeature PaperArticle

Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie

by Andrei Khrennikov

Entropy 2023, 25(11), 1565; https://0-doi-org.brum.beds.ac.uk/10.3390/e25111565 - 20 Nov 2023

Cited by 1 | Viewed by 842

Abstract

We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviews of D’Agostino). Following Helmholtz, Hertz established the “Bild conception” for scientific [...] Read more.

We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviews of D’Agostino). Following Helmholtz, Hertz established the “Bild conception” for scientific theories. Here, “Bild” (“picture”) carries the meaning “model” (mathematical). The main aim of natural sciences is construction of the causal theoretical models (CTMs) of natural phenomena. Hertz claimed that a CTM cannot be designed solely on the basis of observational data; it typically contains hidden quantities. Experimental data can be described by an observational model (OM), often based on the price of acausality. CTM-OM interrelation can be tricky. Schrödinger used the Bild concept to create a CTM for quantum mechanics (QM), and QM was treated as OM. We follow him and suggest a special CTM for QM, so-called prequantum classical statistical field theory (PCSFT). QM can be considered as a PCSFT image, but not as straightforward as in Bell’s model with hidden variables. The common interpretation of the violation of the Bell inequality is criticized from the perspective of the two-level structuring of scientific theories. Such critical analysis of von Neumann and Bell no-go theorems for hidden variables was performed already by De Broglie (and Lochak) in the 1970s. The Bild approach is applied to the two-level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. In classical mechanics, CTM=OM; on the one hand, this is very convenient; on the other hand, this exceptional coincidence blurred the general CTM-OM structuring of scientific theories. We briefly discuss ontic–epistemic structuring of scientific theories (Primas–Atmanspacher) and its relation to the Bild concept. Interestingly, Atmanspacher as well as Hertz claim that even classical physical theories should be presented on the basic of two-level structuring. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

10 pages, 556 KiB

Open AccessArticle

Large Coherent States Formed from Disordered k-Regular Random Graphs

by Gregory D. Scholes

Entropy 2023, 25(11), 1519; https://0-doi-org.brum.beds.ac.uk/10.3390/e25111519 - 06 Nov 2023

Viewed by 946

Abstract

The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust [...] Read more.

The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

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21 pages, 486 KiB

Open AccessArticle

Experimental Predictions for Norm-Conserving Spontaneous Collapse

by D. W. Snoke and D. N. Maienshein

Entropy 2023, 25(11), 1489; https://0-doi-org.brum.beds.ac.uk/10.3390/e25111489 - 27 Oct 2023

Cited by 1 | Viewed by 776

Abstract

Previous work has shown that nonlocal collapse in quantum mechanics can be described by a deterministic, non-unitary operator added to the standard Schrödinger equation. In terms of key aspects, this term differs from prior work on spontaneous collapse. In this paper, we discuss [...] Read more.

Previous work has shown that nonlocal collapse in quantum mechanics can be described by a deterministic, non-unitary operator added to the standard Schrödinger equation. In terms of key aspects, this term differs from prior work on spontaneous collapse. In this paper, we discuss the possible predictions of this model that can be tested by experiments. This class of collapse model does not intrinsically imply unique experimental predictions, but it allows for the possibility. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

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Review

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17 pages, 578 KiB

Open AccessReview

Quantum Nonlocality: How Does Nature Do It?

by Marian Kupczynski

Entropy 2024, 26(3), 191; https://0-doi-org.brum.beds.ac.uk/10.3390/e26030191 - 23 Feb 2024

Cited by 2 | Viewed by 1163

Abstract

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality [...] Read more.

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other’s state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell–CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter’s freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

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18 pages, 274 KiB

Open AccessReview

The Ontology of Haag’s Local Quantum Physics

by Gregg Jaeger

Entropy 2024, 26(1), 33; https://0-doi-org.brum.beds.ac.uk/10.3390/e26010033 - 28 Dec 2023

Viewed by 975

Abstract

The ontology of Local Quantum Physics, Rudolf Haag’s framework for relativistic quantum theory, is reviewed and discussed. It is one of spatiotemporally localized events and unlocalized causal intermediaries, including the elementary particles, which come progressively into existence in accordance with a fundamental arrow [...] Read more.

The ontology of Local Quantum Physics, Rudolf Haag’s framework for relativistic quantum theory, is reviewed and discussed. It is one of spatiotemporally localized events and unlocalized causal intermediaries, including the elementary particles, which come progressively into existence in accordance with a fundamental arrow of time. Haag’s conception of quantum theory is distinguished from others in which events are also central, especially those of Niels Bohr and John Wheeler, with which it has been compared. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)

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