## Entanglement Entropy in Casual Set Theory

Yasaman Yazdi, Perimeter Institute and University of Waterloo

Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore important that we understand it in the context of causal sets. Most definitions of entanglement entropy rely on quantities defined on hypersurfaces. Since canonical data on a hypersurface are not defined in causal sets, we need a spacetime definition of entanglement entropy. Recently, such a definition has been found for a scalar field in a Gaussian state, that expresses the entropy in terms of the field's spacetime correlation function. In this case, the cutoff that renders the entropy finite is also of a spacetime and Lorentz-invariant nature. I will present results from the application of this new definition to causal sets in 1+1 dimensions, finding in particular that the entropy obeys a spacetime-volume law instead of the expected (spatial) area law. I will discuss how one might recover an area law, and I will describe results, from the application of this definition to continuum spacetimes and other discrete models, which provide further clues to the significance of the causal set results.

## Phenomenology of Discrete Spacetime

Alessio Belenchia, International School for Advanced Studies (SISSA)

In this talk I will discuss the phenomenology related to causal sets non-locality, which characterizes the propagation of massless fields on causal sets. After a brief review of causal sets theory, I will introduce a family of non-local wave operators and their properties. Then, I will discuss the response of Unruh-DeWitt detectors couple to non-local field theories of the kind encountered in causal sets theory, showing their power-law dependence on the non- locality scale. Finally, I will show how using non-relativistic opto-mechanical systems it will be possible to cast stringent constraints on non-local theories.

[1] A. Belenchia, D. M. T. Benincasa, and S. Liberati, “Nonlocal Scalar Quantum Field Theory from Causal Sets,” JHEP, vol. 03, p. 036, 2015.

[2] A. Belenchia, D. M. T. Benincasa, S. Liberati, F. Marin, F. Marino, and A. Ortolan, “Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscilla- tors,” Accepted for publication in Phys.Rev.Lett., 2015.

[3] A. Belenchia, D. M. T. Benincasa, E. Martin-Martinez, and M. Saravani, “Detectors in Non-local field theory,” In preparation, 2016.

## Certified Randomness in a Relativistic Quantum Field

Le Phuc Thinh, Centre for Quantum Technologies and QuTech

We will discuss the subtleties that appear in some setups designed to generate randomness out of quantum systems when considering a fully relativistic perspective.

Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well- characterized devices: measuring a quantum system in a basis complementary to its preparation. Towards realizing this goal one may consider using atoms or superconducting qubits, promising candidates for quantum information processing.

However, atomic or superconducting systems unavoidably interact with the electromagnetic field affects their dynamics. This is especially true of systems that can be controlled well enough to perform reliable operations. At large time scales, this interaction can result in decoherence. Smaller time scales in principle avoid this problem, but may not be well analyzed under the usual rotating wave and single-mode approximation which break the relativistic nature of quantum field theory.

Here, we use a fully relativistic analysis to quantify the information that an adversary with access to the field could get on the result of an atomic measurement.

Surprisingly, we find that the adversary’s guessing probability is not minimized for atoms initially prepared in the ground state, as opposed to the intuition that could have been derived from the rotating wave and single mode approximation model.

## Universality of Black Hole Quantum Computing

Benedikt Richter, LMU Munich and IST Lisbon

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.

## A Glimpse of The Early Universe Without Real Light

Ana Blasco, Universidad Complutense de Madrid

The strong Huygens principle states that the radiation Green's function has support only on the light cone [1,2]. In the context of relativistic quantum communication, the violation of this principle implies that there can be a leakage of information towards the inside of the light cone, even for massless quantum fields [3]. When this happens much more information reaches us through timelike channels (not mediated by real photons) than it is carried by rays of light, which are usually regarded as the only carriers of information. In this talk, we will discuss how this has unexpected consequences in cosmological scenarios both in a standard cosmological model (in general relativity) and in the presence of a big bounce which removes the relativistic big bang singularity [4,5]. We will focus on the propagation of information from the early universe to the current era.

[1] R. McLenaghan, Ann. Inst. H. Poincare 20, 153 (1974).

[2] S. Czapor and R. McLenaghan, Acta. Phys. Pol. B Proc.Suppl. 1, 55 (2008).

[3] R. H. Jonsson, E. MartínMartínez, and A. Kempf, Phys. Rev. Lett. 114, 110505 (2015).

[4] A. Blasco, L. J. Garay, M. MartínBenito, and E. MartínMartínez, Phys. Rev. Lett. 114, 141103 (2015). [5] A. Blasco, L. J. Garay, M. MartínBenito, and E. MartínMartínez, Phys. Rev. D 93, 024055 (2016).

Work in collaboration with: L. J. Garay, M. MartínBenito, and E. MartínMartínez

## Concomitant frequencies: amplifying the Unruh effect

Aida Ahmadzadegan, University of Waterloo and Macquarie University

We explore the possibility of amplifying the response of a particle detector to the Unruh effect by optimizing its trajectory and energy gap. To this end, we take advantage of a phenomenon in the Fourier transform of chirped signals. Namely, the Fourier transform of a chirped signal contains not only the frequencies between its initial and final frequencies but with substantial amplitudes also a range of frequencies further outside that range. We call these "concomitant frequencies". By choosing a suitable family of functions for the trajectory and energy gap of the detector, the aim is to strengthen the amplitudes of certain concomitant frequencies, which then enhance the excitation probability of detectors.

## Scalar Fields in a Shell: The Response of An Unruh-Dewitt Detector Inside, and What It Means for Us Outside

Keith Ng, University of Waterloo

We show that a particle detector can distinguish the interior of a hollow shell from flat space for switching times much shorter than the light-crossing time of the shell, even though the local metrics are indistinguishable. This shows that a particle detector can read out information about the non-local structure of spacetime even when switched on for scales much shorter than the characteristic scale of the non-locality.

## Mode Invisibility as a Probe for Quantum States

Marvy Onuma-Kalu, University of Waterloo

## Black Hole Field Theory with a Firewall

C.T. Marco Ho, University of Queensland

In this talk, I will introduce our proposal that the state of a scalar field around a black hole is a modified Unruh vacuum [1]. In (1+1) dimensions we show that a free-faller close to the black hole horizon can be modelled as an inertial observer in a modified Minkowski vacuum state. Using a Gaussian detector centred at a frequency of k, we find that the expectation value of the number operator for a detector crossing the horizon is proportional to 1/|k()| implying a free-faller will observe unbounded numbers of high energy particles, i.e. a firewall. The modification involves implementing a cutoff which we determine by requiring that it preserves Hawking radiation for low frequencies while enabling higher frequencies to carry information out of the black hole. We find that the radiation observed by the free-faller is in a squeezed state.

## Nowhere to Hide: A Study on Evaporating Black Holes Formation and Information Loss

Valentina Baccetti, Macquarie University

The discovery by Hawking (1974) that black holes can emit incoherent radiation at a temperature inversely proportional to their mass, had both completed thermodynamics and introduced the renowned *information loss problem*. For the past forty years this issue has been at the centre of intense debates about unitarity, information and the validity of equivalence principle.

None of the numerous resolutions has provided a definite answer to the issue. A broad class of approaches, from the horizon complementarity to ER=EPR and firewalls, argues for the information recovery by using only the matter sector. However the viewpoint has several problematic features, one of which is to assign a special role to the horizon: It separates the observers, arguably enabling to ignore quantum-mechanical results like, for instance, the no-cloning theorem.

We explore an alternative approached based on the observation that, according to a distant observer, the collapse takes and infinite amount of time while the evaporation time is finite. We follow the collapse of a spherical massive shell and assume that the evaporation starts when the shell is at some finite distance from the Schwarzschild radius 2M. The goal of our analysis is to understand whether, from its own reference frame, the shell evaporates before crossing the intended horizon.

Conceptually, while this model demonstrates the absence of information loss, it forces us to tackle the hard-to-solve fully-coupled gravity-matter problem.

## Particle Generation by Gravitational Perturbations Around a Black Hole

Diaqin Su, University of Queensland

It is well known that plane gravitational waves in Minkowski background spacetime cannot generate particles [1], analogous to that plane electromagnetic waves cannot produce electron-positron pairs [2]. It would be interesting to show whether this is also true in general curved background spacetimes. We study the particle production by the gravitational perturbations around a Schwarzschild black hole. The gravitational perturbations around a black hole are characterized by the quasinormal modes which oscillate with particular frequencies and also damp due to the emission of gravitational waves to the spatial infinity and into the event horizon. We show that the gravitational perturbations around a black hole can produce particles, which is exactly a multimode squeezing process. The gravitational perturbations act as a nonlinear medium and also a pump field. The generated particle number depends on the amplitude and the quality factor of the quasinormal modes. For the Schwarzschild black hole, the damping of the quasinormal modes is large so the particle generation efficiency is very small. While for the extreme Kerr black hole, there exists very low damping quasinormal modes [3] and we expect that there would be substantial particle generation.

Note: This work is a collaboration with Marco Ho, Timothy Ralph and Robert Mann

[1] G. W. Gibbons, Commun. Math. Phys. 45, 191 (1975).

[2] J. Schwinger, Phys. Rev. 82, 664 (1951).

[3] H. Yang, A. Zimmerman and L. Lehner, Phy. Rev. Lett. 114, 081101(2015).