Achim Kempf

A bstract: We propose a scheme by which a wavelet bulk description of a quantum field theory (QFT) can be equipped with a metric based on local multiscale correlation functions. The metric is obtained from the infinitesimal behaviour of the Petz-Rényi mutual information, which is computed from correlations that have been transformed with the continuous wavelet transform. The method presented is applicable to any quadratic QFT that need not be a conformal field theory (CFT). For thermal free scalar and Dirac field theories the resulting metric is that of (asymmetrically) warped Euclidean anti-de Sitter (AdS) space. For massless CFTs in the ground state, the geometry reduces to Euclidean AdS space reminiscent of the usual holographic correspondence. Certain parameters of the resulting geometry can be tuned by changing the shape of the wavelet function while maintaining the same type of geometry.

We show that, during adiabatic evolution, any changes in entanglement can be attributed to a succession of avoided energy level crossings at which eigenvalues swap their eigenvectors. These swaps mediate the generation and redistribution of entanglement in multipartite systems. The efficiency of this redistribution depends on the narrowness of the avoided level crossings and thus constrains the speed of adiabatic evolution. Moreover, we relate the amount of entanglement involved to the ruggedness of the energy landscape, which directly affects the hardness of a computational problem. This enables an analysis of computational complexity and quantum advantage from the point of view of entanglement requirements. Applied to adiabatic quantum computation, our findings directly relate the computation’s speed to its utilization of entanglement as a resource. The same principles extend to gate-based discretized adiabatic quantum algorithms, including those for Hamiltonian simulation and combinatorial optimization.

Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar []. In this work, we identify the optimal waveforms for distinguishing the range resolution between two reflectors of identical strength, leveraging results in quantum metrology. We discuss both the unnormalized optimal waveform as well as the best square-integrable pulse and their variants. Using orthogonal function theory, we give an explicit algorithm to optimize the wave pulse in finite time to have the best performance. We also explore range resolution estimation with unnormalized waveforms with multiparameter methods to also independently estimate loss and time of arrival. These results are consistent with the earlier single parameter approach of range resolution only and give deeper insight into the ranging estimation problem. Experimental results are presented using radio pulse reflections inside coaxial cables, showing robust range resolution smaller than a tenth of the inverse bandlimit, with uncertainties close to the derived Cramér-Rao bound. Published by the American Physical Society 2024

Zusammenfassung: Das Vakuum ist nicht völlig leer, denn die Heisenbergsche Unschärferelation erzwingt Vakuumfluktuationen. Deren Existenz ist über Messungen der Casimir‐Kraft belegt. Folglich muss auch Energie in den Vakuumfluktuationen stecken, die sich nach E = mc² in Form von Gravitation bemerkbar machen sollte. Nach der Allgemeinen Relativitätstheorie müsste ihre Gravitation die Expansion des Universums beschleunigen. Allerdings wäre die Gravitationswirkung, die sich theoretisch aus der quantenmechanisch ermittelten Grundzustandsenergie des Vakuums ergibt, um etwa 120 Gröβenordnungen zu groβ. Dieser Widerspruch ist eine der grundlegenden, ungeklärten Fragestellungen der Physik. Auf der Suche nach einer Antwort soll das Archimedes‐Experiment als extrem empfindliche Waage die Energiedichte des Vakuums bestimmen. Das Resultat soll Hinweise auf die Ursache des „Problems der kosmologischen Konstante” liefern.

Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon sampling theorem from signal processing. Conflicting assumptions in general relativity (smooth spacetime) and quantum field theory (high-energy deviations from low-energy emergent smoothness) motivate the use of such an appealing analytical tool that could thread the needle to meet both requirements. Bandlimited continuous quantum fields are isomorphic to lattice theories—yet without requiring a fixed lattice. Any lattice with a required minimum spacing can be used. This is an isomorphism that avoids taking the limit of the lattice spacing going to zero. In this work, we explore the consequences of this isomorphism, including the emergence of effectively continuous symmetries in quantum lattice theories. One obtains conserved lattice observables for these continuous (Noether) symmetries, as well as a duality of locality from the two perspectives. We expect this work and its extensions to provide useful tools for considering numerical lattice models of continuous quantum fields (e.g., lattice gauge theories) arising from the availability of discreteness without a fixed lattice, as well as offering new insights into emergent continuous symmetries in lattice models and possible laboratory demonstrations of these phenomena.

We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to also describe physical regimes that do not admit position bases. These physical regimes are pregeometric in the sense that they do not admit a mathematical representation of the physical degrees of freedom in terms of fields that live on a spacetime. In regimes in which a spacetime representation does emerge, the geometric properties of the emergent spacetime, such as its dimension and volume, depend on the balance of fermionic pressure and bosonic and gravitational pull. That balance depends, at any given energy scale, on the number of bosonic and fermionic species that contribute, which in turn depends on their masses. This yields an explicit mechanism by which the effective spacetime dimension can depend on the energy scale.

We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to describe also physical regimes that do not admit position bases. These physical regimes are pre-geometric in the sense that they do not admit a mathematical representation of the physical degrees of freedom in terms of fields that live on a spacetime. In regimes in which a spacetime representation does emerge, the geometric properties of the emergent spacetime, such as its dimension and volume, depend on the balance of fermionic pressure and bosonic and gravitational pull. That balance depends, at any given energy scale, on the number of bosonic and fermionic species that contribute, which in turn depends on their masses. This yields an explicit mechanism by which the effective spacetime dimension can depend on the energy scale.