Eduardo Martin-Martinez

Unruh effect in quantum information beyond the single-mode approximation

We address the validity of the single-mode approximation that is commonly invoked in the analysis of entanglement in noninertial frames and in other relativistic quantum-information scenarios. We show that the single-mode approximation is not valid for arbitrary states, finding corrections to previous studies beyond such approximations in the bosonic and fermionic cases. We also exhibit a class of wave packets for which the single-mode approximation is justified subject to the peaking constraints set by an appropriate Fourier transform.

Unveiling quantum entanglement degradation near a Schwarzschild black hole

We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Robs entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation.

Fundamental quantum optics experiments conceivable with satellites : reaching relativistic distances and velocities

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 m (Dimopoulos 2007 Phys. Rev. Lett. 98 111102; 2008 Phys. Rev. D 78 042003). In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ~10−20 m, up to that of hundreds of kilometres (Ursin et al 2007 Nature Phys. 3 481–6). Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.

Entanglement of Dirac fields in an expanding spacetime

We study the entanglement generated between Dirac modes in a 2-dimensional conformally flat Robertson-Walker universe. We find radical qualitative differences between the bosonic and fermionic entanglement generated by the expansion. The particular way in which fermionic fields get entangled encodes more information about the underlying spacetime than the bosonic case, thereby allowing us to reconstruct the parameters of the history of the expansion. This highlights the importance of bosonic/fermionic statistics to account for relativistic effects on the entanglement of quantum fields.

Using Berry's phase to detect the Unruh effect at lower accelerations.

We show that a detector acquires a Berry phase due to its motion in spacetime. The phase is different in the inertial and accelerated case as a direct consequence of the Unruh effect. We exploit this fact to design a novel method to measure the Unruh effect. Surprisingly, the effect is detectable for accelerations 10(9) times smaller than previous proposals sustained only for times of nanoseconds.

Redistribution of particle and antiparticle entanglement in noninertial frames

We analyze the entanglement tradeoff between particle and antiparticle modes of a Dirac field from the perspective of inertial and uniformly accelerated observers. Our results show that a redistribution of entanglement between particle and antiparticle modes plays a key role in the survival of femionic field entanglement in the infinite-acceleration limit.

Spin and occupation number entanglement of Dirac fields for noninertial observers

We investigate the Unruh effect on entanglement taking into account the spin degree of freedom of the Dirac field. We analyze spin Bell states in this setting, obtaining their entanglement dependence on the acceleration of one of the partners. Then, we consider simple analogs to the occupation number entangled state |00>+|11> but with spin quantum numbers for |11>. We show that, despite their apparent similitude, while the spinless case is always qubitxqubit, for the spin case acceleration produces a qubitxfour-level quantum system state. We also introduce a procedure to consistently erase the spin information from our setting preserving occupation numbers. We show how the maximally entangled state for occupation number emerges from our setting. We as well analyze its entanglement dependence on acceleration, obtaining greater entanglement degradation than in the spinless case.

Quantum correlations through event horizons: Fermionic versus bosonic entanglement

We disclose the behavior of quantum and classical correlations among all the different spatial-temporal regions of a space-time with an event horizon, comparing fermionic with bosonic fields. We show the emergence of conservation laws for entanglement and classical correlations, pointing out the crucial role that statistics plays in the information exchange (and more specifically, the entanglement tradeoff) across horizons. The results obtained here could shed new light on the problem of information behavior in noninertial frames and in the presence of horizons, giving better insight into the black-hole information paradox.

Cosmological quantum entanglement

We review recent literature on the connection between quantum entanglement and cosmology, with an emphasis on the context of expanding universes. We discuss recent theoretical results reporting on the production of entanglement in quantum fields due to the expansion of the underlying spacetime. We explore how these results are affected by the statistics of the field (bosonic or fermionic), the type of expansion (de Sitter or asymptotically stationary), and the coupling to spacetime curvature (conformal or minimal). We then consider the extraction of entanglement from a quantum field by coupling to local detectors and how this procedure can be used to distinguish curvature from heating by their entanglement signature. We review the role played by quantum fluctuations in the early universe in nucleating the formation of galaxies and other cosmic structures through their conversion into classical density anisotropies during and after inflation. We report on current literature attempting to account for this transition in a rigorous way and discuss the importance of entanglement and decoherence in this process. We conclude with some prospects for further theoretical and experimental research in this area. These include extensions of current theoretical efforts, possible future observational pursuits, and experimental analogues that emulate these cosmic effects in a laboratory setting.

Fermionic entanglement that survives a black hole

We introduce an arbitrary number of accessible modes when analyzing bipartite entanglement degradation due to Unruh effect between two partners Alice and Rob. Under the single mode approximation (SMA) a fermion field only had a few accessible levels due to Pauli exclusion principle conversely to bosonic fields which had an infinite number of excitable levels. This was argued to justify entanglement survival in the fermionic case in the SMA infinite acceleration limit. Here we relax SMA. Hence, an infinite number of modes are excited as the observer Rob accelerates, even for a fermion field. We will prove that, despite this analogy with the bosonic case, entanglement loss is limited. We will show that this comes from fermionic statistics through the characteristic structure it imposes on the infinite dimensional density matrix for Rob. Surprisingly, the surviving entanglement is independent of the specific maximally entangled state chosen, the kind of fermionic field analyzed, and the number of accessible modes considered. We shall discuss whether this surviving entanglement goes beyond the purely statistical correlations, giving insight concerning the black hole information paradox.