Weekly Papers on Quantum Foundations (38)

Authors: Ippei DanshitaMasanori HanadaMasaki Tezuka

The realization of quantum field theories on an optical lattice is an important subject toward the quantum simulation. We argue that such efforts would lead to the experimental realizations of quantum black holes. The basic idea is to construct non-gravitational systems which are equivalent to the quantum gravitational systems via the holographic principle. Here the `equivalence’ means that two theories cannot be distinguished even in principle. Therefore, if the holographic principle is true, one can create actual quantum black holes by engineering the non-gravitational systems on an optical lattice. In this presentation, we consider the simplest example: the Sachdev-Ye-Kitaev (SYK) model. We design an experimental scheme for creating the SYK model with use of ultra-cold fermionic atoms such as Lithium-6.

Authors: Mario BertaFernando G. S. L. BrandaoChristoph Hirche

We extend quantum Stein’s lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states $\rho^{\otimes n}$ against convex combinations of quantum states $\sigma^{\otimes n}$ is given by a regularized quantum relative entropy distance formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes a novel operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite Stein’s lemma for classical probability distributions and lift the result to the non-commutative setting by only using elementary properties of quantum entropy. Finally, our findings also imply an improved Markov type lower bound on the quantum conditional mutual information in terms of the regularized quantum relative entropy – featuring an explicit and universal recovery map.

Authors: Yakir AharonovEliahu CohenJeff Tollaksen

Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest “atoms”? In the following paper we answer these questions on the negative for a specific class of systems and measurements. We begin with simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to new surprising effects within atomic and electromagnetic systems. A general construction based on pre- and post-selected ensembles is then suggested, where the N-body correlation can be genuinely perceived as a global property, as long as one is limited to preforming a small set of measurements which we term “strictly local”. We conclude that within time-symmetric quantum mechanics and under certain boundary conditions, high-order correlations can determine low-order ones, but not vice versa. Moreover, the latter seem to provide no information at all regarding the former. This supports a top-down structure in many-body quantum mechanics.

Authors: Saurya DasMatthew P. G. RobbinsElias C. Vagenas

It is believed that classical behavior emerges in a quantum system due to decoherence. It has also been proposed that gravity can be a source of this decoherence. We examine this in detail by studying a number of quantum systems, including ultra-relativistic and non-relativistic particles, at low and high temperatures in an expanding Universe, and show that this proposal is valid for a large class of quantum systems.

Fletcher, Samuel C. and Manchak, John Byron and Schneider, Mike D. and Weatherall, James Owen (2017) Would Two Dimensions be World Enough for Spacetime? [Preprint]
Chibbaro, Sergio and Vulpiani, Angelo (2017) Compressibility, laws of nature, initial conditions and complexity. [Preprint]

Authors: Peter Morgan

Manifestly Lorentz covariant representations of the algebras of the quantized electromagnetic field and of the observables of the quantized Dirac spinor field are constructed that act on Hilbert spaces that are generated using classical random fields acting on a vacuum state, allowing a comparatively classical interpretation of the states of the theory.

Authors: Pasquale Bosso

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canon ical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.

Authors: Bassam HelouYanbei Chen

Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, testing the limits of standard quantum mechanics, and reconciling it with gravity. Two results substantially undermined the credibility of non-linear theories. Some have been experimentally refuted, and more importantly, all deterministic non-linear theories can be used for superluminal communication. However, these results are unconvincing because they overlook the fact that the distribution of measurement results predicted by non-linear quantum mechanics depends on the interpretation of quantum mechanics that one uses. For instance, although the Everett and Copenhagen interpretations agree on the expression of Born’s rule for the outcomes of multiple measurements in linear quantum mechanics, they disagree in non-linear quantum mechanics. We present the range of expressions of Born’s rule that can be obtained by applying different formulations of quantum mechanics to a class of non-linear quantum theories. We then determine that many do not allow for superluminal communication but only two seem to have a reasonable justification. The first is the Everett interpretation, and the second, which we name causal-conditional, states that a measurement broadcasts its outcome to degrees of freedom in its future light-cone, who update the wavefunction that their non-linear Hamiltonian depends on according to this new information.

Wuthrich, Christian (2017) Are black holes about information? [Preprint]

The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space and time, and would strengthen the existing analogy between quantum states and classical probability distributions. Under the assumption that the joint state over time is an operator on the tensor product of single-time Hilbert spaces, we analyse various proposals for such a joint state, including one due to Leifer and Spekkens, one due to Fitzsimons, Jones and Vedral, and another based on discrete Wigner functions. Finding various problems with each, we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time steps is associative. We show that no construction satisfies all these requirements. If Hermiticity is dropped, then there is an essentially unique construction that satisfies the remaining four criteria.

Authors: Sreenath K. ManikandanAndrew N. Jordan

We establish an analogy between superconductor-metal interfaces and the quantum physics of a black hole, using the proximity effect. We show that the metal-superconductor interface can be thought of as an event horizon and Andreev reflection from the interface is analogous to the Hawking radiation in black holes. We describe quantum information transfer in Andreev reflection with a final state projection model similar to the Horowitz-Maldacena model for black hole evaporation. We also propose the Andreev reflection-analogue of Hayden and Preskill’s description of a black hole final state, where the black hole is described as an information mirror. The analogy between Crossed Andreev Reflections and Einstein-Rosen bridges is discussed: our proposal gives a precise mechanism for the apparent loss of quantum information in a black hole by the process of nonlocal Andreev reflection, transferring the quantum information through a wormhole and into another universe. Given these established connections, we conjecture that the final quantum state of a black hole is exactly the same as the ground state wavefunction of the superconductor/superfluid in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity; in particular, the infalling matter and the infalling Hawking quanta, described in the Horowitz-Maldacena model, forms a Cooper pair-like singlet state inside the black hole. A black hole evaporating and shrinking in size can be thought of as the analogue of Andreev reflection by a hole where the superconductor loses a Cooper pair. Our model does not suffer from the black hole information problem since Andreev reflection is unitary. We also relate the thermodynamic properties of a black hole to that of a superconductor, and propose an experiment which can demonstrate the negative specific heat feature of black holes in a growing/evaporating condensate.

Authors: Don Weingarten

We propose a method for finding an initial state vector which by ordinary Hamiltonian time evolution follows a single branch of many-worlds quantum mechanics. The resulting deterministic system appears to exhibit random behavior as a result of the successive emergence over time of information present in the initial state but not previously observed.

Authors: Juan Campos Quemada

The aim of this essay is to analyze the role of quantum mechanics as an inherent characteristic of life. During the last ten years the problem of the origin of life has become an innovative research subject approached by many authors. The essay is divided in to three parts: the first deals with the problem of life from a philosophical and biological perspective. The second presents the conceptual and methodological basis of the essay which is founded on the Information Theory and the Quantum Theory. This basis is then used, in the third part, to discuss the different arguments and conjectures of a quantum origin of life. There are many philosophical views on the problem of life, two of which are especially important at the moment: reductive physicalism and biosystemic emergentism. From a scientific perspective, all the theories and experimental evidences put forward by Biology can be summed up in to two main research themes: the RNA world and the vesicular theory. The RNA world, from a physicalist point of view, maintains that replication is the essence of life while the vesicular theory, founded on biosystemic grounds, believes the essence of life can be found in cellular metabolism. This essay uses the Information Theory to discard the idea of a spontaneous emergency of life through replication. Understanding the nature and basis of quantum mechanics is fundamental in order to be able to comprehend the advantages of using quantum computation to be able increase the probabilities of existence of auto replicative structures. Different arguments are set forth such as the inherence of quantum mechanics to the origin of life. Finally, in order to try to resolve the question of auto replication, three scientific propositions are put forward: Q-life, the quantum combinatory library and the role of algorithms in the origin of genetic language.

Authors: Michael K.-H. Kiessling

This is an invited review of Jean Bricmont’s book “Making Sense of Quantum Mechanics.”

Authors: Atsushi HiguchiSatoshi IsoKazushige UedaKazuhiro Yamamoto

The Minkowski vacuum state is expressed as an entangled state between the left and right Rindler wedges when it is constructed on the Rindler vacuum. In this paper, we further examine the entanglement structure and extend the expression to the future (expanding) and past (shrinking) Kasner spacetimes. This clarifies the origin of the quantum radiation produced by an Unruh–DeWitt detector in uniformly accelerated motion in the four-dimensional Minkowski spacetime. We also investigate the two-dimensional massless case where the quantum radiation vanishes but the same entanglement structure exists.

Author(s): Lev Vaidman, Alon Ben-Israel, Jan Dziewior, Lukas Knips, Mira Weißl, Jasmin Meinecke, Christian Schwemmer, Ran Ber, and Harald Weinfurter

It is argued that a weak value of an observable is a robust property of a single pre- and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affected other systems as if it had been in an eigenstate with eigenvalue equal to t…
[Phys. Rev. A 96, 032114] Published Tue Sep 19, 2017

Author(s): Mark M. Wilde, Marco Tomamichel, Seth Lloyd, and Mario Berta

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis…
[Phys. Rev. Lett. 119, 120501] Published Mon Sep 18, 2017

Nature Physics. doi:10.1038/nphys4256

Author: Elisabetta Collini

By engineering photosensitive proteins and tweaking the classical properties of light, it should be possible to tune the response of a cell equipped with photoreceptors. But would these cells be able to sense the subtle quantum properties of light?

Nature Physics. doi:10.1038/nphys4257

Authors: Kush Paul, Parijat Sengupta, Eugene D. Ark, Haohua Tu, Youbo Zhao & Stephen A. Boppart

Retinal-based opsins are light-sensitive proteins. The photoisomerization reaction of these proteins has been studied outside cellular environments using ultrashort tailored light pulses. However, how living cell functions can be modulated via opsins by modifying fundamental nonlinear optical properties of light interacting with the retinal chromophore has remained largely unexplored. We report the use of chirped ultrashort near-infrared pulses to modulate light-evoked ionic current from Channelrhodopsin-2 (ChR2) in brain tissue, and consequently the firing pattern of neurons, by manipulating the phase of the spectral components of the light. These results confirm that quantum coherence of the retinal-based protein system, even in a living neuron, can influence its current output, and open up the possibilities of using designer-tailored pulses for controlling molecular dynamics of opsins in living tissue to selectively enhance or suppress neuronal function for adaptive feedback-loop applications in the future.

Authors: Eugenio MegiasMariano QuirosLindber Salas

We study the recently found anomalies in $B$-meson decays within a scenario with a warped extra dimension where the Standard Model fermions are propagating in the bulk. The anomalies are then interpreted as the result of the exchange of heavy vector resonances with electroweak quantum numbers. The model naturally leads to lepton-flavor universality violation when different flavor fermions are differently localized along the extra dimension, signaling a different degree of compositeness in the dual holographic theory.

Authors: Alessandro Strumia

The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and states. Extending this reasoning suggests an interpretation of quantum mechanics generalized with indefinite quantum norm.

de Ronde, Christian (2016) Quantum Superpositions and the Representation of Physical Reality Beyond Measurement Outcomes and Mathematical Structures. [Preprint]

Experimental Non-Violation of the Bell Inequality

A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry IU in cosmological state space. Consistent with the assumed primacy of IU, and p-adic number theory, a non-Euclidean (and hence non-classical) metric gp is defined on cosmological state space, where p is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be gp-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit p=, at which gp is Euclidean. Broader implications are discussed.

Comments: arXiv admin note: text overlap with arXiv:1709.00329
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:1709.01069 [quant-ph]

A Gravitational Theory of the Quantum

The synthesis of quantum and gravitational physics is sought through a finite, realistic, locally causal theory where gravity plays a vital role not only during decoherent measurement but also during non-decoherent unitary evolution. Invariant set theory is built on geometric properties of a compact fractal-like subsetIU of cosmological state space on which the universe is assumed to evolve and from which the laws of physics are assumed to derive. Consistent with the primacy of IU, a non-Euclidean (and hence non-classical) state-space metric gp is defined, related to the p-adic metric of number theory where p is a large but finite Pythagorean prime. Uncertain states on IU are described using complex Hilbert states, but only if their squared amplitudes are rational and corresponding complex phase angles are rational multiples of 2π. Such Hilbert states are necessarily gp-distant from states with either irrational squared amplitudes or irrational phase angles. The gappy fractal nature of IU accounts for quantum complementarity and is characterised numerically by a generic number-theoretic incommensurateness between rational angles and rational cosines of angles. The Bell inequality, whose violation would be inconsistent with local realism, is shown to be gp-distant from all forms of the inequality that are violated in any finite-precision experiment. The delayed-choice paradox is resolved through the computational irreducibility of IU. The Schr\”odinger and Dirac equations describe evolution on IU in the singular limit at p=. By contrast, an extension of the Einstein field equations on IU is proposed which reduces smoothly to general relativity as p. Novel proposals for the dark universe and the elimination of classical space-time singularities are given and experimental implications outlined.

Subjects: General Physics (physics.gen-ph); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
Cite as: arXiv:1709.00329 [physics.gen-ph]


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