arXiv subjects

Achim Kempf

Publications and source records attributed to Achim Kempf.

At least 55 records · Page 3Linked to original sources

arXiv2020

Transmission of quantum information through quantum fields

We investigate the quantum channel consisting of two localized quantum systems that communicate through a scalar quantum field. We choose a scalar field rather than a tensor or vector field, such as the electromagnetic field, in order to isolate the situation where the qubits are carried by the field amplitudes themselves rather than, for example, by encoding qubits in the polarization of photons. We find that suitable protocols for this type of quantum channel require the careful navigation of several constraints, such as the no-cloning principle, the strong Huygens principle and the tendency of short field-matter couplings to be entanglement breaking. We non-perturbatively construct a protocol for such a quantum channel that possesses maximal quantum capacity.

quant-ph↗

arXiv2020

Which part of the stress-energy tensor gravitates?

We consider the possibility that, in the semiclassical Einstein equation for cosmological spacetimes, gravity is sourced by the amount of stress-energy that is above that of the instantaneous ground state. For this possibility to be consistent, the Bianchi identities must continue to hold. This is nontrivial because it means that the ground state expectation value of the stress-energy tensor must be covariantly conserved in spite of the fact that the ground state is generally a different state at different times. We prove that this consistency condition does hold. As a consequence, we find that the vacuum stress-energy which is above the instantaneous ground state does not renormalize the cosmological constant, as long as the instantaneous ground states and the instantaneous adiabatic vacua exist.

gr-qc↗

arXiv2019

On Coherent Delocalization in the Light-Matter Interaction

We investigate how the coherent spreading of the center of mass wave function of a particle, such as an atom, molecule or ion, affects the particle's interaction with fields such as the electromagnetic field or a phonon field, in view also of possible applications to emerging quantum technologies. To this end, we develop a suitably generalized Unruh-deWitt model for the interaction between a delocalizing first quantized particle and a second quantized field. We study how the coherent spreading of the center of mass wave function of the particle affects emission and absorption rates and we find, in particular, that in the case of a supersonic coherent spreading in a medium, there should occur Cherenkov-like emissions, along with the excitation of the particle.

quant-ph↗

arXiv2019

Probing geometric information using the Unruh effect in the vacuum

We present a new method by which, in principle, it is possible to "see in absolute darkness," i.e., without exchanging any real quanta through quantum fields. This is possible because objects modify the mode structure of the vacuum in their vicinity. The new method probes the mode structure of the vacuum through the Unruh effect, i.e., by recording the excitation rates of quantum systems that are accelerated.

gr-qc↗

arXiv2019

Quantum imaging using relativistic detectors

Imaging in quantum optics (QO) is usually formulated in the languages of quantum mechanics and Fourier optics. While relatively advanced fields, notions such as different reference frames and the degradation of entanglement due to acceleration do not usually feature. Here we propose the idea of using so-called Unruh-DeWitt (UDW) detectors to model the imaging process in QO. In particular, we first present a quantum field theory version of a state describing Spontaneous Parametric Down Conversion (SPDC), one of the principal processes employed to create entangled photons in the laboratory. This state, coupled to UDW detectors, is used to investigate a single-pixel ghost image under both inertial and non-inertial settings, and a two-pixel image under inertial conditions. The reconstructed images obtained for various possible inputs can be distinguished better than a pure guess, hence the formalism can be used to describe imaging between non-inertial frames. We briefly consider the origin of the correlations between the UDW detectors, which don't appear to arise from the usual notion of entanglement. Finally, we find that the contrast between the possible outcomes in the single-pixel case follows a curious coupling time dependent behaviour.

quant-ph↗

arXiv2019

Zeno Friction and Anti-friction from Quantum Collision Models

We analyze the quantum mechanics of the friction experienced by a small system as it moves non-destructively with velocity $v$ over a surface. Specifically, we model the interactions between the system and the surface with a \textit{collision model}. We show that, under weak assumptions, the magnitude of the friction induced by this interaction decreases as $1/v$ for large velocities. Specifically, we predict that this phenomenon occurs in the Zeno regime, where each of the system's successive couplings to subsystems of the surface is very brief. In order to investigate the friction at low velocities and with velocity-dependent coupling strengths, we motivate and develop \textit{one-dimensional convex collision models}. Within these models, we obtain an analytic expression for the general friction-velocity dependence. We are thus able to determine exactly the conditions under which the usual friction-velocity dependency arises. Finally, we give examples that demonstrate the possibility, in principle, of anti-friction, in which case the system is accelerated by its interaction with the surface, a phenomenon associated with active materials and inverted level populations.

quant-ph↗

arXiv2018

Quantum Shockwave Communication

We present a scheme to produce shockwaves in quantum fields by means of pretimed emitters. We find that by suitably pre-entangeling the emitters, the shockwave's energy density can be locally modulated and amplified. When the large amplitudes in such a shockwave are used for communication, the channel capacity depends not only on the signal-to-noise ratio but also on the effect that the entanglement of the emitters has on the correlations in the signal and in the quantum noise at the receiver. As a consequence, by choosing the entanglement of the emitters, the flow of information in the shockwave can be modulated and spatially shaped to some extent independently of the flow of energy. We also find that there exists a finite optimal strength of the coupling between the receiver and the quantum field which optimizes the channel capacity by optimizing the tradeoff between sensitivity to the signal and sensitivity to the coupling-induced quantum noise.

quant-ph↗

arXiv2018

On the Unruh effect, trajectories and information

We calculate the trajectories which maximize the Unruh effect, mode by mode, when given a fixed energy budget for acceleration. We find that Unruh processes are most likely to occur, and therefore potentially best observable, for certain trajectories whose acceleration is not uniform. In practice, the precise form of optimal trajectories depends on experimental bounds on how fast the acceleration can be changed. We also show that the Unruh spectra of arbitrarily accelerated observers contain the complete information to reconstruct the observers' trajectories.

gr-qc↗

arXiv2018

Transmitting qubits through relativistic fields

Wireless communication derives its power from the simultaneous emission of signals in multiple directions. However, in the context of quantum communication, this phenomenon must be reconciled carefully with the no-cloning principle. In this context, we here study how wireless communication of quantum information can be realized via relativistic fields. To this end, we extend existing frameworks to allow for a non-perturbative description of, e.g., quantum state transfer. We consider, in particular, the case of 1+1 spacetime dimensions, which already allows a number of interesting scenarios, pointing to, for example, new methods for tasks similar to quantum secret sharing.

quant-ph↗

arXiv2018

Jumping champions and prime gaps using information-theoretic tools

We study the spacing of the primes using methods from information theory. In information theory, the equivalence of continuous and discrete representations of information is established by Shannon sampling theory. Here, we use Shannon sampling methods to construct continuous functions whose varying bandwidth follows the distribution of the prime numbers. The Fourier transforms of these signals spike at frequently occurring spacings between the primes. We find prominent spikes, in particular, at the primorials. Previously, the primorials have been conjectured to be the most frequent gaps between subsequent primes, the so-called "jumping champions". Here, we find a foreshadowing of the primorial's role as jumping champions in the sense that Fourier spikes for the primorials arise much earlier on the number axis than where the primorials in question are expected to reign as jumping champions.

math.NT↗

arXiv2018

Quantum gravity, information theory and the CMB

We review connections between the metric of spacetime and the quantum fluctuations of fields. In particular, we discuss the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlators of the fluctuations of quantum fields. We also discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of the diffeomorphism group. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.

gr-qc↗

arXiv2018

A classification of open Gaussian dynamics

We introduce a classification scheme for the generators of bosonic open Gaussian dynamics, providing instructive diagrams description for each type of dynamics. Using this classification, we discuss the consequences of imposing complete positivity on Gaussian dynamics. In particular, we show that non-symplectic operations must be active to allow for complete positivity. In addition, non-symplectic operations can, in fact, conserve the volume of phase space only if the restriction of complete positivity is lifted. We then discuss the implications for the relationship between information and energy flows in open quantum mechanics.

quant-ph↗

arXiv2018

Gaussian ancillary bombardment

We analyze in full detail the time evolution of an open Gaussian quantum system rapidly bombarded by Gaussian ancillae. As a particular case this analysis covers the thermalization (or not) of a harmonic oscillator coupled to a thermal reservoir made of harmonic oscillators. We derive general results for this scenario and apply them to the problem of thermalization. We show that only a particular family of system-environment couplings will cause the system to thermalize to the temperature of its environment. We discuss that if we want to understand thermalization as ensuing from the Markovian interaction of a system with the individual microconstituents of its (thermal) environment then the process of thermalization is not as robust as one might expect.

quant-ph↗

arXiv2018

Four Aspects of Superoscillations

A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of superoscillations: 1. Superoscillations can be generated efficiently and stably through multiplication. 2. There is a win-win situation in the sense that even in circumstances where superoscillations cannot be used for superresolution, they can be useful for what may be called superabsorption, an effective up-conversion of low frequencies 3. The study of superoscillations may be useful for generalizing the Shannon Hartley noisy channel capacity theorem. 4. The phenomenon of superoscillations naturally generalizes beyond bandlimited functions.

math-ph↗

arXiv2017

A Convexity Result in the Spectral Geometry of Conformally Equivalent Metrics on Surfaces

Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this end, we study analytic paths of metrics that induce isospectral Laplace-Beltrami operators over oriented compact surfaces without boundary. Applying perturbation theory, we show that sets of conformally equivalent metrics on such surfaces contain no nontrivial convex subsets. This indicates that cases where the manifolds cannot be reconstructed from their spectra are highly constrained.

math.DG↗

arXiv2017

Stabilizing quantum dynamics through coupling to a quantized environment

We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an environment, we derive a lower bound on the fidelity decay, which increases with increasing uncertainty in the state of the environment. Remarkably, this robustness in fidelity can be achieved even in fragile chaotic systems. We show that non-Markovianity is necessary for attaining robustness in the fidelity.

quant-ph↗

arXiv2017

Natural Covariant Planck Scale Cutoffs and the Cosmic Microwave Background Spectrum

We calculate the impact of quantum gravity-motivated ultraviolet cutoffs on inflationary predictions for the cosmic microwave background spectrum. We model the ultraviolet cutoffs fully covariantly to avoid possible artifacts of covariance breaking. Imposing these covariant cutoffs results in the production of small, characteristically $k-$dependent oscillations in the spectrum. The size of the effect scales linearly with the ratio of the Planck to Hubble lengths during inflation. Consequently, the relative size of the effect could be as large as one part in $10^5$; i.e., eventual observability may not be ruled out.

gr-qc↗

arXiv2017

Integration by differentiation: new proofs, methods and examples

Recently, new methods were introduced which allow one to solve ordinary integrals by performing only derivatives. These studies were originally motivated by the difficulties of the quantum field theoretic path integral, and correspondingly, the results were derived by heuristic methods. Here, we give rigorous proofs for the methods to hold on fully specified function spaces. We then illustrate the efficacy of the new methods by applying them to the study of the surprising behavior of so-called Borwein integrals.

math-ph↗