arXiv subjects

Ulvi Yurtsever

Publications and source records attributed to Ulvi Yurtsever.

27 records · Page 2Linked to original sources

arXiv2002

Interferometry with Entangled Atoms

A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. Laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two motion-sensitive phase shifts which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here I propose entangling the quantum states of the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase which can be measured directly, with no need for differencing.

quant-ph↗

arXiv2000

Quantum Mechanics and Algorithmic Randomness

A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost certainly, genuinely (algorithmically) random. This result can be interpreted as a strengthening of Bell's no-hidden-variables theorem, and relies on causality and quantum entanglement in a manner similar to Bell's original argument.

quant-ph↗

arXiv2000

A Lorentz-invariant look at quantum clock synchronization protocols based on distributed entanglement

Recent work has raised the possibility that quantum information theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state which then needs to be purified asynchronously. We present a fully relativistic analysis of the QCS protocol which shows that asynchronous entanglement purification is not possible, and, therefore, that the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum information theory which may lead to a complete, working QCS protocol.

quant-ph↗

arXiv1995

A note on the averaged null energy condition in quantum field theory

The averaged null energy condition has been recently shown to hold for linear quantum fields in a large class of spacetimes. Nevertheless, it is easy to show by using a simple scaling argument that ANEC as stated cannot hold generically in curved four-dimensional spacetime, and this scaling argument has been widely interpreted as a death-blow for averaged energy conditions in quantum field theory. In this note I propose a simple generalization of ANEC, in which the right-hand-side of the ANEC inequality is replaced by a finite (but in general negative) state-independent lower bound. As long as attention is focused on asymptotically well-behaved spacetimes, this generalized version of ANEC is safe from the threat of the scaling argument, and thus stands a chance of being generally valid in four-dimensional curved spacetime. I argue that when generalized ANEC holds, it has implications for the non-negativity of total energy and for singularity theorems similar to the implications of ANEC. In particular, I show that if generalized ANEC is satisfied in static traversable wormhole spacetimes (which is likely but remains to be shown), then macroscopic wormholes (but not necessarily microscopic, Planck-size wormholes) are ruled out by quantum field theory.

gr-qc↗

arXiv1994

Geometry of chaos in the two-center problem in General Relativity

The now-famous Majumdar-Papapetrou exact solution of the Einstein-Maxwell equations describes, in general, $N$ static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When $N=2$, this solution defines the two-black-hole spacetime, and the relativistic two-center problem is the problem of geodesic motion on this static background. Contopoulos and a number of other workers have recently discovered through numerical experiments that in contrast with the Newtonian two-center problem, where the dynamics is completely integrable, relativistic null-geodesic motion on the two black-hole spacetime exhibits chaotic behavior. Here I identify the geometric sources of this chaotic dynamics by first reducing the problem to that of geodesic motion on a negatively curved (Riemannian) surface.

gr-qc↗

arXiv1994

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.

gr-qc↗

arXiv1994

A remark on kinks and time machines

We describe an elementary proof that a manifold with the topology of the Politzer time machine does not admit a nonsingular, asymptotically flat Lorentz metric.

gr-qc↗

arXiv1993

Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. In the algebraic formulation of linear quantum field theory, the canonical commutation relations are restated in terms of a well-defined symplectic structure on the space of smooth solutions, and the local field algebra is constructed as the Weyl algebra associated to this symplectic vector space. When spacetime is not globally hyperbolic, e.g. when it contains naked singularities or closed timelike curves, a global Cauchy surface does not exist, and there is no obvious way to formulate the canonical commutation relations, hence no obvious way to construct the field algebra. In a paper submitted elsewhere, we report on a generalization of the algebraic framework for quantum field theory to arbitrary topological spaces which do not necessarily have a spacetime metric defined on them at the outset. Taking this generalization as a starting point, in this paper we give a prescription for constructing the field algebra of a (massless or massive) Klein-Gordon field on an arbitrary background spacetime. When spacetime is globally hyperbolic, the theory defined by our construction coincides with the ordinary Klein-Gordon field theory on a

gr-qc↗

arXiv1993

The origin of spacetime topology and generalizations of quantum field theory

The research effort reported in this paper is directed, in a broad sense, towards understanding the small-scale structure of spacetime. The fundamental question that guides our discussion is ``what is the physical content of spacetime topology?" In classical physics, if spacetime, $(X, τ)$, has sufficiently regular topology, and if sufficiently many fields exist to allow us to observe all continuous functions on $X$, then this collection of continuous functions uniquely determines both the set of points $X$ and the topology $τ$ on it. To explore the small-scale structure of spacetime, we are led to consider the physical fields (the observables) not as classical (continuous functions) but as quantum operators, and the fundamental observable as not the collection of all continuous functions but the local algebra of quantum field operators. In pursuing our approach further, we develop a number of generalizations of quantum field theory through which it becomes possible to talk about quantum fields defined on arbitrary topological spaces. Our ultimate generalization dispenses with the fixed background topological space altogether and proposes that the fundamental observable should be taken as a lattice (or more specifically a ``frame," in the sense of set theory) of closed subalgebras of an abstract $C^{\ast}$ algebra. Our discussion concludes with the definition and some elementary

gr-qc↗