Model for Emergence of Spacetime from Fluctuations.

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.

Super Interferometric Range Resolution.

We probe the fundamental underpinnings of range resolution in coherent remote sensing. We use a novel class of self-referential interference functions to show that we can greatly improve upon currently accepted bounds for range resolution. We consider the range resolution problem from the perspective of single-parameter estimation of amplitude versus the traditional temporally resolved paradigm. We define two figures of merit: (i) the minimum resolvable distance between two depths and (ii) for temporally subresolved peaks, the depth resolution between the objects. We experimentally demonstrate that our system can resolve two depths greater than 100× the inverse bandwidth and measure the distance between two objects to approximately 20 µm (35 000 times smaller than the Rayleigh-resolved limit) for temporally subresolved objects using frequencies less than 120 MHz radio waves.

Acceleration-Induced Effects in Stimulated Light-Matter Interactions.

We show that, in addition to the Unruh effect, there exist two new phenomena that are due to acceleration in the quantum theory of the light-matter interaction. The first is the phenomenon of acceleration-induced transparency which arises since acceleration impacts not only the counter-rotating terms in the light-matter interaction (the cause of the conventional Unruh effect) but also the rotating wave terms. The second new phenomenon is that the Unruh effect can be stimulated, a phenomenon that arises since not only rotating-wave terms can be stimulated (as in conventional stimulated emission) but also counter-rotating terms. The new phenomena are potentially strong enough to be experimentally observable.

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.

Correlation-Enhanced Algorithmic Cooling.

We propose a method for increasing the purity of interacting quantum systems that takes advantage of correlations present due to the internal interaction. In particular, when this interaction is sufficiently strong, we show that by using the system's quantum correlations one can achieve cooling beyond established limits of previous conventional algorithmic cooling proposals which assume no interaction.

Information transmission without energy exchange.

We show that it is possible to use a massless field in the vacuum to communicate in such a way that the signal travels arbitrarily slower than the speed of light and such that no energy is transmitted from the sender to the receiver. Instead, the receiver has to supply a signal-dependent amount of work to switch his detector on and off. This type of communication is related to Casimir-like interactions, and it is made possible by dimension-and curvature-dependent subtleties of Huygens' principle.

Shape from sound: toward new tools for quantum gravity.

To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at least in the case of the Euclidean signature, is the discipline of spectral geometry. It aims at describing curved manifolds in terms of the spectra of their canonical differential operators. As an immediate benefit, this would offer a clean gauge-independent identification of the metric's degrees of freedom in terms of invariants that should be ready to quantize. However, spectral geometry is itself hard and has been plagued by ambiguities. Here, we regularize and break up spectral geometry into small, finite-dimensional and therefore manageable steps. We constructively demonstrate that this strategy works at least in two dimensions. We can now calculate the shapes of two-dimensional objects from their vibrational spectra.

Processing quantum information with relativistic motion of atoms.

We show that particle detectors, such as two-level atoms, in noninertial motion (or in gravitational fields) could be used to build quantum gates for the processing of quantum information. Concretely, we show that through suitably chosen noninertial trajectories of the detectors the interaction Hamiltonian's time dependence can be modulated to yield arbitrary rotations in the Bloch sphere due to relativistic quantum effects.

Neural networks can learn to utilize correlated auxiliary noise.

We demonstrate that neural networks that process noisy data can learn to exploit, when available, access to auxiliary noise that is correlated with the noise on the data. In effect, the network learns to use the correlated auxiliary noise as an approximate key to decipher its noisy input data. An example of naturally occurring correlated auxiliary noise is the noise due to decoherence. Our results could, therefore, also be of interest, for example, for machine-learned quantum error correction.

Information-theoretic natural ultraviolet cutoff for spacetime.

Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can. It has been shown that the amplitudes phi(x(n)) that a field takes at a generic discrete set of points x(n) can be sufficient to reconstruct the field phi(x) for all x, namely, if there exists a certain type of natural ultraviolet (UV) cutoff in nature, and if the average spacing of the sample points is at the UV-cutoff scale. Here, we generalize this information-theoretic framework to spacetimes themselves. We show that samples taken at a generic discrete set of points of a Euclidean-signature spacetime can allow one to reconstruct the shape of that spacetime everywhere, down to the cutoff scale. The resulting methods could be useful in various approaches to quantum gravity.

Information theory, spectral geometry, and quantum gravity.

We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.

Error-reducing structure of the genetic code indicates code origin in non-thermophile organisms.

During the RNA World, organisms experienced high rates of genetic errors, which implies that there was strong evolutionary pressure to reduce the errors' phenotypical impact by suitably structuring the still-evolving genetic code. Therefore, the relative rates of the various types of genetic errors should have left characteristic imprints in the structure of the genetic code. Here, we show that, therefore, it is possible to some extent to reconstruct those error rates, as well as the nucleotide frequencies, for the time when the code was fixed. We find evidence indicating that the frequencies of G and C in the genome were not elevated. Since, for thermodynamic reasons, RNA in thermophiles tends to possess elevated G+C content, this result indicates that the fixation of the genetic code occurred in organisms which were either not thermophiles or that the code's fixation occurred after the rise of DNA.

Generalization of quantum error correction via the Heisenberg picture.

We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may therefore suitably be called "operator algebra quantum error correction"). In particular, the approach provides a framework for the correction of hybrid quantum-classical information and it does not require the state to be entirely in one of the corresponding subspaces or subsystems. We discuss applications to quantum teleportation and to the study of information flows in quantum interactions.

Covariant information-density cutoff in curved space-time.

In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.