Search Results (79)

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data $p\left(M|D\right)$, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates $p\left(D|M\right)$, the likelihood of the data under the model, which undermines the importance of low-ℓ physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article

Conformal field theory is quantized on the ideal boundary of a Riemann surface, and the effect on the widths of the resonances of the quantum states is evaluated. The resonances on a surface can be recast in terms of eigenfunctions of a differential operator on the Mandelstam plane. Cusps in this plane, representing Landau singularities, reflect a divergence in the coupling. A cusp on the Riemann surface similarly causes a divergence in the scattering amplitude. The interpretation of the string diagram indicates that the self-interaction of the string in the vicinity of the cusp causes it to implode, which would require an infinite coupling. A consistent physical interpretation of cusps on surfaces requires supersymmetry. The study of unitary minimal models and N = 2 superminimal models indicates that there can exist a set of resonances at the cusps and ends of the surfaces. The uncertainty in the masses of six types of particles at a finite set of cusps is infinitesimal. Tachyon condensation on the ideal boundary would introduce an uncertainty in the mass of a charged particle. The widths of charged particle resonances at the ends of infinite-genus surfaces is not negligible and can be traced to the coupling with tachyons. Full article

We pose and address the radical question of whether quantum mechanics, known for its firm internal structure and enormous empirical success, carries in itself the genomes of larger quantum theories that have higher internal intricacy and phenomenological versatility. In other words, we consider, at the basic level of closed quantum systems and regardless of interpretational aspects, whether standard quantum theory (SQT) harbors quantum theories with context-based deformed principles or structures, having definite predictive power within much broader scopes. We answer this question in the affirmative following complementary evidence and reasoning arising from quantum-computation-based quantum simulation and fundamental, general, and abstract rationales within the frameworks of information theory, fundamental or functional emergence, and participatory agency. In this light, as we show, one is led to the recently proposed experience-centric quantum theory (ECQT), which is a larger and richer theory of quantum behaviors with drastically generalized quantum dynamics. ECQT allows the quantum information of the closed quantum system’s developed state history to continually contribute to defining and updating the many-body interactions, the Hamiltonians, and even the internal elements and “particles” of the total system. Hence, the unitary evolutions are continually impacted and become guidable by the agent system’s experience. The intrinsic interplay of unitarity and non-Markovianity in ECQT brings about a host of diverse behavioral phases, which concurrently infuse closed and open quantum system characteristics, and it even surpasses the theory of open systems in SQT. From a broader perspective, a focus of our investigation is the existence of the quantum interactome—the interactive landscape of all coexisting, independent, context-based quantum theories that emerge from inferential participatory agencies—and its predictive phenomenological utility. Full article

We present a theoretical investigation into the expansion dynamics of Rydberg-dressed ultracold Fermi gases. The effective interaction potential induced by Rydberg dressing significantly modifies the intrinsic properties and dynamical behavior of the quantum gas. The strength and range of these interactions can be precisely tuned by varying the intensity and detuning of the applied laser field. By employing mean-field theory and utilizing the density distribution of the atomic cloud to describe the quantum system dynamics, we theoretically describe the time-dependent evolution of the atomic cloud during the free expansion process, encompassing both non-interacting and unitary Fermi gases. Notably, the specific quantum states of the ground-state atoms play a pivotal role in shaping the effective interaction potential within the Rydberg-dressed quantum system. We elucidate how the interaction potential influences the rate and mode of the atom cloud’s expansion by hydrodynamic expansion arising from Rydberg-dressed atoms in distinct spin hyperfine states. This investigation may deepen our understanding of the behavior and interactions in quantum many-body systems and offer broad potential for future applications like the exploration of novel quantum phase transitions and emergent phenomena. Full article

In a number of previous publications, scattering theory for N-pole semiconductor quantum devices was developed. In the framework of the Landauer–Büttiker formalism, an S-matrix was constructed with the aid of an R-matrix providing a mapping of the in-going waves onto the out-going waves. These waves include propagating waves and evanescent waves, the latter of which decay exponentially in the leads which are connected to the active region of the N-pole device. In order to formulate the current conservation in the N-pole device, it is necessary to define the current S-matrix schematically as $\tilde{S}=k^{1/2}S{k}^{-1/2}$, where k contains the information about the k-vectors of the mentioned in- and out-going waves. In this paper, we show how the complete current S-matrix is calculated including the coupling between the propagating and evanescent components and coupling to the bound states in the active device region. One then finds a sub-matrix of $\tilde{S}$ which is unitary and which is restricted to the space of the propagating components. We demonstrate that current conservation is associated with the unitarity just of this sub-matrix. Full article

In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian $H^{\left(IC\right)}=p^2+\mathrm{i}{x}^3$ does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic exceptional point” (IEP) features of $H^{\left(IC\right)}$ and, in particular, to the phenomenon of a high-energy asymptotic parallelization of its bound-state-mimicking eigenvectors. In this paper, it is argued that the operator $H^{\left(IC\right)}$ (and the like) can only be interpreted as a manifestly unphysical, singular IEP limit of a hypothetical one-parametric family of certain standard quantum Hamiltonians. For explanation, ample use is made of perturbation theory and of multiple analogies between IEPs and conventional Kato’s exceptional points. Full article

We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum/classical VQS, END/QC/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END/QC/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = −1/2. We illustrate an END/QC/VQS simulation with the pure electronic dynamics of H₂⁺ We discuss the present results and future END/QC/QVS extensions. Full article

In the de Broglie Bohm pilot-wave theory and the many-worlds interpretation, unitary development of the quantum state is universally valid. They differ in that de Broglie and Bohm assumed that there are point particles with positions that evolve in time and that our observations are observations of the particles. The many-worlds interpretation is based on the fact that the quantum state can explain our observations. Both interpretations rely on the decoherence mechanism to explain the disappearance of interference effects at a measurement. From this fact, it is argued that for the pilot-wave theory to work, circumstances must be such that the many-worlds interpretation is a viable alternative. However, if this is the case, the de Broglie–Bohm particles become irrelevant to any observer. They are truly hidden. The violation of locality and the corresponding violation of Lorenz invariance are good reasons to believe that dBB particles do not exist. Full article

Before we ask what the quantum gravity theory is, there is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems, especially unitarity loss (pure states evolving into mixed states), have raised concerns over several decades. In this paper, acknowledging the fact that time is a parameter in quantum theory, which is different from its status in the context of General Relativity (GR), we start with a “quantum first approach” and propose a new formulation for QFTCS based on the discrete spacetime transformations which offer a way to achieve unitarity. We rewrite the QFT in Minkowski spacetime with a direct-sum Fock space structure based on the discrete spacetime transformations and geometric superselection rules. Applying this framework to QFTCS, in the context of de Sitter (dS) spacetime, we elucidate how this approach to quantization complies with unitarity and the observer complementarity principle. We then comment on understanding the scattering of states in de Sitter spacetime. Furthermore, we discuss briefly the implications of our QFTCS approach to future research in quantum gravity. Full article

Wigner’s classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to the theory of ordinary unitary representations by enlarging the group of physical symmetries. Nevertheless, the enlargement process is not always described explicitly: it is unclear in which cases the enlargement has to be conducted on the universal cover, a central extension, or a central extension of the universal cover. On the other hand, in the mathematical literature, projective unitary representations have been extensively studied, and famous theorems such as the theorems of Bargmann and Cassinelli have been achieved. The present article bridges the two: we provide a precise, step-by-step guide on describing projective unitary representations as unitary representations of the enlarged group. Particular focus is paid to the difference between algebraic and topological obstructions. To build the bridge mentioned above, we present a detailed review of the difference between group cohomology and Lie group cohomology. This culminates in classifying Lie group central extensions by smooth cocycles around the identity. Finally, the take-away message is a hands-on algorithm that takes the symmetry group of a given quantum theory as input and provides the enlarged group as output. This algorithm is applied to several cases of physical interest. We also briefly outline a generalization of Bargmann’s theory to time-dependent phases using Hilbert bundles. Full article

A quantum theory of mesoscopic circuits, based on the discreteness of electric charges, was recently proposed. However, it is not applied widely, mainly because of the difficulty of the mathematical solution to the finite-difference Schrödinger equation. In this paper, we propose an improved perturbation method to calculate Schrödinger equations of the inductance and capacity coupling mesoscopic circuit. With a unitary transformation, the finite differential Schrödinger equation of the system is divided into two equations in generalized momentum representation. The concrete value of the parameter in circuits is important to solving the equation. Both the perturbation method suitable case and the improved perturbation method suitable case, the wave functions, and energy level of the system are achieved. As an application, the current fluctuations are calculated and discussed. The improved mathematical method would be helpful for the popularization of the quantum circuits theory. Full article

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et al. This approach modifies Wigner’s method by introducing an arbitrary timelike unit vector $n^{\mu }$ and then inducing a representation of $SL(2,C)$, based on $p^{\mu }$ rather than on the spacetime momentum. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^{\mu },p^{\mu }),({\zeta }^{\mu },{\pi }^{\mu })\}$, inducing a representation on the momentum ${\pi }^{\mu }$, thus providing a novel dynamical interpretation of the timelike unit vector $n^{\mu }={\pi }^{\mu }/M$. Studying the unitary representations of the Poincaré group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments. Full article

In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation. Full article

Concurrence is a crucial entanglement measure in quantum theory used to describe the degree of entanglement between two or more qubits. Local unitary (LU) invariants can be employed to describe the relevant properties of quantum states. Compared to quantum state tomography, observing LU invariants can save substantial physical resources and reduce errors associated with tomography. In this paper, we use LU invariants as explanatory variables and employ methods such as multiple regression, tree models, and BP neural network models to fit the concurrence of 2-qubit quantum states. For pure states and Werner states, by analyzing the correlation between data, a functional formula for concurrence in terms of LU invariants is obtained. Additionally, for any two-qubit quantum states, the prediction accuracy for concurrence reaches 98.5%. Full article

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements. Full article