Journal Description
Quantum Reports
Quantum Reports
is an international, peer-reviewed, open access journal on quantum science. It publishes original research articles and review articles in all quantum subfields, from basic quantum theory to a broad array of applications. Quantum Reports is published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus and other databases.
- Journal Rank: CiteScore - Q2 (Physics and Astronomy (miscellaneous))
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 22.4 days after submission; acceptance to publication is undertaken in 5.6 days (median values for papers published in this journal in the first half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Latest Articles
Applications of Supersymmetric Polynomials in Statistical Quantum Physics
Quantum Rep. 2023, 5(4), 683-697; https://doi.org/10.3390/quantum5040043 (registering DOI) - 08 Dec 2023
Abstract
We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences Such an approach
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We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for , induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations.
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(This article belongs to the Special Issue Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models)
Open AccessArticle
A Schrödinger Equation for Evolutionary Dynamics
by
, , , , , , and
Quantum Rep. 2023, 5(4), 659-682; https://doi.org/10.3390/quantum5040042 - 31 Oct 2023
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We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore,
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We establish an analogy between the Fokker–Planck equation describing evolutionary landscape dynamics and the Schrödinger equation which characterizes quantum mechanical particles, showing that a population with multiple genetic traits evolves analogously to a wavefunction under a multi-dimensional energy potential in imaginary time. Furthermore, we discover within this analogy that the stationary population distribution on the landscape corresponds exactly to the ground-state wavefunction. This mathematical equivalence grants entry to a wide range of analytical tools developed by the quantum mechanics community, such as the Rayleigh–Ritz variational method and the Rayleigh–Schrödinger perturbation theory, allowing us not only the conduct of reasonable quantitative assessments but also exploration of fundamental biological inquiries. We demonstrate the effectiveness of these tools by estimating the population success on landscapes where precise answers are elusive, and unveiling the ecological consequences of stress-induced mutagenesis—a prevalent evolutionary mechanism in pathogenic and neoplastic systems. We show that, even in an unchanging environment, a sharp mutational burst resulting from stress can always be advantageous, while a gradual increase only enhances population size when the number of relevant evolving traits is limited. Our interdisciplinary approach offers novel insights, opening up new avenues for deeper understanding and predictive capability regarding the complex dynamics of evolving populations.
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Open AccessArticle
Variational Amplitude Amplification for Solving QUBO Problems
Quantum Rep. 2023, 5(4), 625-658; https://doi.org/10.3390/quantum5040041 - 01 Oct 2023
Abstract
We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on quadratic unconstrained binary optimization (QUBO) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate
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We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on quadratic unconstrained binary optimization (QUBO) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as ‘cost oracle’ operations , which distribute phases across the basis states proportional to a cost function. We then show that when is combined with the standard Grover diffusion operator , one can achieve high probabilities of measurement for states corresponding to optimal and near optimal solutions while still only requiring O( ) iterations. In order to achieve these probabilities, a single scalar parameter is required, which we show can be found through a variational quantum–classical hybrid approach and can be used for heuristic solutions.
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(This article belongs to the Special Issue Quantum Computing: A Taxonomy, Systematic Review, and Future Directions)
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Open AccessArticle
Reality Does Not Shine, It Twinkles
Quantum Rep. 2023, 5(4), 609-624; https://doi.org/10.3390/quantum5040040 - 25 Sep 2023
Abstract
Arguments have been made that the violation of the CHSH and similar inequalities shows that reality at the quantum level must be non-local. The derivation of Bell inequality is re-examined, and it is shown that violations of these inequalities merely demonstrate the existence
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Arguments have been made that the violation of the CHSH and similar inequalities shows that reality at the quantum level must be non-local. The derivation of Bell inequality is re-examined, and it is shown that violations of these inequalities merely demonstrate the existence of contextuality—they say nothing about the causal influences underlying such contextuality. It is argued that contextual systems do not possess enduring (propositional) properties, merely contingent properties. An example of a classical situation is presented: a two-player co-operative game, the random variables of which are consistently connected in the sense of Dzhafarov, which is contextual, and violates the CHSH inequality. In fact, it also violates the Tsirel’son bound. The key is that this system is generated, and its properties are disposed of, not determined.
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Open AccessReview
Research Trends in Quantum Computers by Focusing on Qubits as Their Building Blocks
Quantum Rep. 2023, 5(3), 597-608; https://doi.org/10.3390/quantum5030039 - 13 Sep 2023
Cited by 1
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Quantum computing is a rapidly developing field that has the potential to revolutionize the way we process data. In this article, we will introduce quantum computers, their hardware and the challenges associated with their development. One of the key concepts in quantum computing
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Quantum computing is a rapidly developing field that has the potential to revolutionize the way we process data. In this article, we will introduce quantum computers, their hardware and the challenges associated with their development. One of the key concepts in quantum computing is the qubit, which is the basic unit of quantum information. We will discuss this concept in greater detail, exploring how qubits work and the unique properties that make them so powerful. There are currently three leading models of quantum computers: superconducting, ion trap, and neutral-atom qubits. We will compare these models, highlighting their respective advantages and limitations, and discuss the current state of research in each area. In addition to exploring the hardware of quantum computers, we will also introduce some of the innovative research projects related to qubits. Finally, we will examine the market around the quantum computing industry, outlining some of the fundamental challenges we may face.
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Open AccessArticle
Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics
by
Quantum Rep. 2023, 5(3), 584-596; https://doi.org/10.3390/quantum5030038 - 11 Sep 2023
Abstract
The deterministic nature of EQM (the Everett Interpretation of Quantum Mechanics) seems to be inconsistent with the use of probability in EQM, giving rise to what is known as the “incoherence problem”. In this paper, I explore approaches to solve the incoherence problem
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The deterministic nature of EQM (the Everett Interpretation of Quantum Mechanics) seems to be inconsistent with the use of probability in EQM, giving rise to what is known as the “incoherence problem”. In this paper, I explore approaches to solve the incoherence problem of EQM via pre-measurement uncertainty. Previous discussions on the validity of pre-measurement uncertainty have leaned heavily on intricate aspects of the theory of semantics and reference, the embrace of either four-dimensionalism or three-dimensionalism of personhood, or the ontology of EQM. In this paper, I argue that, regardless of the adoption of three-dimensionalism or four-dimensionalism of personhood, the overlapping view or the divergence view of the ontology of EQM, the pre-measurement uncertainty approach to the incoherence problem of EQM can only achive success while contradicting fundamental principles of physicalism. I also use the divergence view of EQM as an example to illustrate my analyses.
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
Open AccessArticle
ATP-Dependent Mismatch Recognition in DNA Replication Mismatch Repair
by
and
Quantum Rep. 2023, 5(3), 565-583; https://doi.org/10.3390/quantum5030037 - 21 Aug 2023
Abstract
Mismatch repair is a critical step in DNA replication that occurs after base selection and proofreading, significantly increasing fidelity. However, the mechanism of mismatch recognition has not been established for any repair enzyme. Speculations in this area mainly focus on exploiting thermodynamic equilibrium
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Mismatch repair is a critical step in DNA replication that occurs after base selection and proofreading, significantly increasing fidelity. However, the mechanism of mismatch recognition has not been established for any repair enzyme. Speculations in this area mainly focus on exploiting thermodynamic equilibrium and free energy. Nevertheless, non-equilibrium processes may play a more significant role in enhancing mismatch recognition accuracy by utilizing adenosine triphosphate (ATP). This study aimed to investigate this possibility. Considering our limited knowledge of actual mismatch repair enzymes, we proposed a hypothetical enzyme that operates as a quantum system with three discrete energy levels. When the enzyme is raised to its highest energy level, a quantum transition occurs, leading to one of two low-energy levels representing potential recognition outcomes: a correct match or a mismatch. The probabilities of the two outcomes are exponentially different, determined by the energy gap between the two low energy levels. By flipping the energy gap, discrimination between mismatches and correct matches can be achieved. Within a framework that combines quantum mechanics with thermodynamics, we established a relationship between energy cost and the recognition error.
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(This article belongs to the Special Issue Recent Advances in Quantum Biology)
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Open AccessArticle
Optical Dromions for Spatiotemporal Fractional Nonlinear System in Quantum Mechanics
Quantum Rep. 2023, 5(3), 546-564; https://doi.org/10.3390/quantum5030036 - 18 Jul 2023
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In physics, mathematics, and other disciplines, new integrable equations have been found using the P-test. Novel insights and discoveries in several domains have resulted from this. Whether a solution is oscillatory, decaying, or expanding exponentially can be observed by using the AEM
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In physics, mathematics, and other disciplines, new integrable equations have been found using the P-test. Novel insights and discoveries in several domains have resulted from this. Whether a solution is oscillatory, decaying, or expanding exponentially can be observed by using the AEM approach. In this work, we examined the integrability of the triple nonlinear fractional Schrödinger equation (TNFSE) via the Painlevé test (P-test) and a number of optical solitary wave solutions such as bright dromions (solitons), hyperbolic, singular, periodic, domain wall, doubly periodic, trigonometric, dark singular, plane-wave solution, combined optical solitons, rational solutions, etc., via the auxiliary equation mapping (AEM) technique. In mathematical physics and in engineering sciences, this equation plays a very important role. Moreover, the graphical representation (3D, 2D, and contour) of the obtained optical solitary-wave solutions will facilitate the understanding of the physical phenomenon of this system. The computational work and conclusions indicate that the suggested approaches are efficient and productive.
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Open AccessArticle
Control Landscape of Measurement-Assisted Transition Probability for a Three-Level Quantum System with Dynamical Symmetry
by
and
Quantum Rep. 2023, 5(3), 526-545; https://doi.org/10.3390/quantum5030035 - 13 Jul 2023
Cited by 1
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Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all
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Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is , whereas it is about using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state.
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Open AccessArticle
Teleportation Revealed
Quantum Rep. 2023, 5(2), 510-525; https://doi.org/10.3390/quantum5020034 - 13 Jun 2023
Abstract
Quantum teleportation is the name of a problem: How can the real-valued parameters encoding the state at Alice’s location make their way to Bob’s location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a
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Quantum teleportation is the name of a problem: How can the real-valued parameters encoding the state at Alice’s location make their way to Bob’s location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schrödinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed.
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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Open AccessArticle
Quantum Probability from Temporal Structure
Quantum Rep. 2023, 5(2), 496-509; https://doi.org/10.3390/quantum5020033 - 12 Jun 2023
Abstract
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In -ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified using fractions of a
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The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In -ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified using fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics, with a network of ‘fixed points’ defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre- and postselection.
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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Open AccessArticle
Kupczynski’s Contextual Locally Causal Probabilistic Models Are Constrained by Bell’s Theorem
Quantum Rep. 2023, 5(2), 481-495; https://doi.org/10.3390/quantum5020032 - 06 Jun 2023
Cited by 1
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In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally
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In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell–CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski’s escape route for local realism is not available.
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Open AccessOpinion
The Everything-Is-a-Quantum-Wave Interpretation of Quantum Physics
Quantum Rep. 2023, 5(2), 475-480; https://doi.org/10.3390/quantum5020031 - 06 Jun 2023
Abstract
In this paper, I would like to outline what I think is the most natural interpretation of quantum mechanics. By natural, I simply mean that it requires the least amount of excess baggage and that it is universal in the sense that it
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In this paper, I would like to outline what I think is the most natural interpretation of quantum mechanics. By natural, I simply mean that it requires the least amount of excess baggage and that it is universal in the sense that it can be consistently applied to all the observed phenomena, including the universe as a whole. I call it the “Everything is a Quantum Wave” Interpretation (EQWI) because I think this is a more appropriate name than the Many Worlds Interpretation (MWI). The paper explains why this is so.
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
Open AccessArticle
Hydrogen-like Plasmas under Endohedral Cavity
Quantum Rep. 2023, 5(2), 459-474; https://doi.org/10.3390/quantum5020030 - 30 May 2023
Cited by 1
Abstract
Over the past few decades, confined quantum systems have emerged to be a subject of considerable importance in physical, chemical and biological sciences. Under such stressed conditions, they display many fascinating and notable physical and chemical properties. Here we address this situation by
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Over the past few decades, confined quantum systems have emerged to be a subject of considerable importance in physical, chemical and biological sciences. Under such stressed conditions, they display many fascinating and notable physical and chemical properties. Here we address this situation by using two plasma models, namely a weakly coupled plasma environment mimicked by a Debye-Hückel potential (DHP) and an exponential cosine screened Coulomb potential (ECSCP). On the other hand, the endohedral confinement is achieved via a Woods-Saxon (WS) potential. The critical screening constant, dipole oscillator strength (OS) and polarizability are investigated for an arbitrary state. A Shannon entropy-based strategy has been invoked to study the phase transition here. An increase in Z leads to larger critical screening. Moreover, a detailed investigation reveals that there exists at least one bound state in such plasmas. Pilot calculations are conducted for some low-lying states ( ) using a generalized pseudo spectral scheme, providing optimal, non-uniform radial discretization.
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(This article belongs to the Topic Theoretical, Quantum and Computational Chemistry)
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Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach
by
, , , , and
Quantum Rep. 2023, 5(2), 442-458; https://doi.org/10.3390/quantum5020029 - 26 May 2023
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We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e.,
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We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet.
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Open AccessArticle
Conditions for Graviton Emission in the Recombination of a Delocalized Mass
Quantum Rep. 2023, 5(2), 426-441; https://doi.org/10.3390/quantum5020028 - 22 May 2023
Cited by 2
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In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles
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In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles with the superposed locations, a proposed resolution being graviton emission from quadrupole moments. Here, we focus on the delocalized particle (forgetting about the probe and the gedanken experiment) and explore the conditions (in terms of mass, separation, and recombination time) for graviton emission. Through this, we find that the variations of quadrupole moments in the recombination are generically greatly enhanced if the field is entangled compared to if it is sourced instead by the energy momentum expectation value on the delocalized state (moment variation in the latter case, with m mass, d separation). In addition, we obtain the (upper) limit recombination time for graviton emission growing as m in place of the naive expectation . In this, the Planck mass acts as threshold mass (huge, for delocalized objects): no graviton emission is possible below it, however fast the recombination occurs. If this is compared with the decay times foreseen in the collapse models of Diósi and Penrose (in their basic form), one finds that no (quadrupole) graviton emission from recombination is possible in them. Indeed, right when m becomes large enough to allow for emission, it also becomes too large for the superposition to survive collapse long enough to recombine.
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Open AccessArticle
The Open Systems View and the Everett Interpretation
Quantum Rep. 2023, 5(2), 418-425; https://doi.org/10.3390/quantum5020027 - 28 Apr 2023
Abstract
It is argued that those who defend the Everett, or ‘many-worlds’, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics.
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It is argued that those who defend the Everett, or ‘many-worlds’, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics. GT is a wider dynamical framework than its alternative, standard quantum theory (ST). This is true even though GT makes no modifications to the quantum formalism. GT rather takes a different view, what we call the open systems view, of the formalism; i.e., in GT, the dynamics of systems whose physical states are fundamentally represented by density operators are represented as fundamentally open as specified by an in general non-unitary dynamical map. This includes, in principle, the dynamics of the universe as a whole. We argue that the more general dynamics describable in GT can be physically motivated, that there is as much prima facie empirical support for GT as there is for ST, and that GT could be fully in the spirit of the Everett interpretation—that there might, in short, be little reason for an Everettian not to embrace the more general theoretical landscape that GT allows one to explore.
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
Open AccessArticle
How Everett Solved the Probability Problem in Everettian Quantum Mechanics
Quantum Rep. 2023, 5(2), 407-417; https://doi.org/10.3390/quantum5020026 - 26 Apr 2023
Abstract
A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on
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A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on the concept of typicality. It argues that Everett’s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett’s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation.
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(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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Open AccessArticle
Leggett–Garg-like Inequalities from a Correlation Matrix Construction
by
and
Quantum Rep. 2023, 5(2), 398-406; https://doi.org/10.3390/quantum5020025 - 23 Apr 2023
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The Leggett–Garg Inequality (LGI) constrains, under certain fundamental assumptions, the correlations between measurements of a quantity Q at different times. Here, we analyze the LGI and propose similar but somewhat more elaborate inequalities, employing a technique that utilizes the mathematical properties of correlation
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The Leggett–Garg Inequality (LGI) constrains, under certain fundamental assumptions, the correlations between measurements of a quantity Q at different times. Here, we analyze the LGI and propose similar but somewhat more elaborate inequalities, employing a technique that utilizes the mathematical properties of correlation matrices, which was recently proposed in the context of nonlocal correlations. We also find that this technique can be applied to inequalities that combine correlations between different times (as in LGI) and correlations between different locations (as in Bell inequalities). All the proposed bounds include additional correlations compared to the original ones and also lead to a particular form of complementarity. A possible experimental realization and some applications are briefly discussed.
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Open AccessArticle
The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics
Quantum Rep. 2023, 5(2), 370-397; https://doi.org/10.3390/quantum5020024 - 20 Apr 2023
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Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present).
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Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schrödinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.
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Exploring Information and Complexity Measures in Quantum Systems by Exactly Solvable Models
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