# Weekly Papers on Quantum Foundations (34)

A central tenant in the classification of phases is that boundary conditions cannot affect the bulk properties of a system. In this work we show striking, yet puzzling, evidence of a clear violation of this assumption. We use the prototypical example of an XYZ chain with no external field in a ring geometry with an odd number of sites and both ferromagnetic and antiferromagnetic interaction. In such setting, we can calculate directly the magnetizations that are traditionally used as order parameters to characterize the phases of the system. When the ferromagnetic interaction dominates, we recover magnetizations that in the thermodynamic limit lose any knowledge about the boundary conditions and are in complete agreement with the standard expectations. On the contrary, when the system is governed by the anti-ferromagnetic interaction, the magnetizations decay algebraically to zero with the system size and it is not staggered, despite the AFM coupling. We term this behavior ferromagnetic mesoscopic magnetization. Hence, in the antiferromagnetic regime, our results show an unexpected dependence of a local, one-point function on the boundary conditions, that is in contrast with the predictions of the general theory.

 上午10:25 | quant-ph updates on arXiv.org

Authors: Yoshiki SatoKento Watanabe

Recently, Chapman et al. argued that holographic complexities for defects distinguish action from volume. Motivated by their work, we study complexity of quantum states in conformal field theory with boundary. In generic two-dimensional BCFT, we work on the path-integral optimization which gives one of field-theoretic definitions for the complexity. We also perform holographic computations of the complexity in Takayanagi’s AdS/BCFT model following by the “complexity $=$ volume conjecture and “complexity $=$ action” conjecture. We find that increments of the complexity due to the boundary do not vanish in these models in contrast to the argument by Chapman et al. Thus, we conclude that boundary does not distinguish the complexities in general.

 上午10:25 | quant-ph updates on arXiv.org

Authors: Shreya P. KumarMartin B. Plenio

Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on concrete experiments involving macroscopic pendula and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.

 上午10:25 | quant-ph updates on arXiv.org

We provide the first evidence that under certain conditions, electrons may naturally behave like a Grover search, looking for defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e. local unitary matrices that drive the evolution of a single particle on the lattice. Some of these are well-known to recover the $(2+1)$–dimensional Dirac equation in continuum limit, i.e. the free propagation of the electron. We study two such Dirac QW, one on the square grid and the other on a triangular grid reminiscent of graphene-like materials. The numerical simulations show that the walker localises around a defect in $O(\sqrt{N})$ steps with probability $O(1/\log{N})$. This in line with previous QW formulations of the Grover search on the 2D grid. But these Dirac QW are naturally occurring’ and require no specific oracle step other than a hole defect in a material.

We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of auxiliary system. Our method utilizes solely: (a) classical randomness and post-processing, (b) projective measurements on a relevant quantum system and (c) postselection on non-observing certain outcomes. The scheme implements arbitrary quantum measurement in dimension $d$ with the optimal success probability $1/d$. We apply our results to bound the relative power of projective and generalised measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on IBM’s quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements generalized qubit measurements outperforms the standard construction using the auxiliary system.

Authors: Detlef DürrSheldon GoldsteinNino Zanghí

Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows one to straightforwardly define a quantum motion, a Bohmian mechanics, on shape space. We show how this motion gives rise to the more or less familiar theory in absolute space and time. We find that free motion on shape space, when lifted to configuration space, becomes an interacting theory. Many different lifts are possible corresponding in fact to different choices of gauges. Taking the laws of Bohmian mechanics on shape space as physically fundamental, we show how the theory can be statistically analyzed by using conditional wave functions, for subsystems of the universe, represented in terms of absolute space and time.

The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measure $N(x_2,x_1;\sigma)$ for the effective number of quantum paths [of length $\sigma$ connecting two events $(x_1,x_2)$] in an arbitrary spacetime. When $x_2=x_1$, this reduces to $C(x,\sigma)$ giving the measure for closed quantum loops of length $\sigma$ containing an event $x$. Both $N(x_2,x_1;\sigma)$ and $C(x,\sigma)$ are well-defined and depend only on the geometry of the spacetime. Various other physical quantities like, for e.g., the effective Lagrangian, can be expressed in terms of $N(x_2,x_1;\sigma)$. The corresponding measure for the total path length contributed by the closed loops, in a spacetime region $\mathcal{V}$, is given by the integral of $L(\sigma;x) \equiv\sigma C(\sigma;x)$ over $\mathcal{V}$. Remarkably enough $L(0;x) \propto R(x)$, the Ricci scalar; i.e, the measure for the total length contributed by infinitesimal closed loops in a region of spacetime gives us the Einstein-Hilbert action. Its variation, when we vary the metric, can provide a new route towards induced/emergent gravity descriptions. In the presence of a background electromagnetic field, the corresponding expressions for $N(x_2,x_1;\sigma)$ and $C(x,\sigma)$ can be related to the holonomies of the field. The measure $N(x_2,x_1;\sigma)$ can also be used to evaluate a wide class of path integrals for which the action and the measure are arbitrary functions of the path length. As an example, I compute a modified path integral which incorporates the zero-point-length in the spacetime. I also describe several other properties of $N(x_2,x_1;\sigma)$ and outline a few simple applications.

 上午10:25 | gr-qc updates on arXiv.org

We consider a scalar field with a bottom-less potential, such as $g^3 \phi$, finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if $g \lesssim 1.2 H_0^{2/3} M_{\rm Pl}^{1/3}$. If rebounces avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics selects a small vacuum energy and becomes the most likely source of universes with anthropically small cosmological constant. Its probability distribution could avoid the gap by 2 orders of magnitude that seems left by standard anthropic selection.

 2019年8月30日 星期五 下午6:00 | André M. Timpanaro, Giacomo Guarnieri, John Goold, and Gabriel T. Landi | PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

Author(s): André M. Timpanaro, Giacomo Guarnieri, John Goold, and Gabriel T. Landi

Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this Letter, we identify the tightest (and saturable) matrix-valued TUR that can be derived from the exchange fluctuation theorems describi…

[Phys. Rev. Lett. 123, 090604] Published Fri Aug 30, 2019

 2019年8月29日 星期四 下午6:00 | Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner | PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

Author(s): Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner

The spin is the prime example of a qubit. Encoding and decoding information in the spin qubit is operationally well defined through the Stern-Gerlach setup in the nonrelativistic (i.e., low velocity) limit. However, an operational definition of the spin in the relativistic regime is missing. The ori…

[Phys. Rev. Lett. 123, 090404] Published Thu Aug 29, 2019

 2019年8月29日 星期四 上午12:00 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Pitts, J. Brian (2019) General Relativity, Mental Causation, and Energy Conservation. [Preprint]
 2019年8月28日 星期三 下午11:56 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Pitts, J. Brian (2019) Cosmological Constant Λ vs. Massive Gravitons: A Case Study in General Relativity Exceptionalism vs. Particle Physics Egalitarianism. [Preprint]
 2019年8月28日 星期三 下午11:55 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Glick, David (2019) QBism and the Limits of Scientific Realism. [Preprint]
 2019年8月28日 星期三 下午3:16 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Muñoz Garganté, Nuria (2019) A Physicist’s Road to Emergence: A Revisited Story of “More Is Different”. In: UNSPECIFIED.
 2019年8月28日 星期三 下午3:14 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Hermens, Ronnie (2019) Completely Real? A Critical Note on the Theorems by Colbeck and Renner. In: UNSPECIFIED.
 2019年8月28日 星期三 下午3:12 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Pitts, J. Brian (2019) The Mind-Body Problem and Conservation Laws: The Growth of Physical Understanding? [Preprint]
 2019年8月28日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

In this paper non-Hausdorff manifolds as potential basic objects of General Relativity are investigated. One can distinguish four stages of identifying an appropriate mathematical structure to describe physical systems: kinematic, dynamical, physical reasonability, and empirical. The thesis of this paper is that in the context of General Relativity, non-Hausdorff manifolds pass the first two stages, as they enable one to define the basic notions of differential geometry needed to pose the problem of the evolution-distribution of matter and are not in conflict with the Einstein equations. With regard to the third stage, various potential conflicts with physical reasonability conditions are considered with a tentative conclusion that non-Hausdorff manifolds are more likely to pass this stage than is typically assumed. When dealing with some of these problems, the modal interpretation of non-Hausdorff manifolds is invoked, according to which they represent bundles of alternative possible spacetimes rather than single spacetimes.

# Bell’s Theorem and Spacetime-Based Reformulations of Quantum Mechanics

In this critical review of Bell’s Theorem, its implications for reformulations of quantum theory are considered. The assumptions of the theorem are set out explicitly, within a framework of mathematical models with well-defined inputs and outputs. Attention is drawn to the assumption that the mathematical quantities associated with a certain time and place can depend on past model inputs (such as preparation settings) but not on future inputs (such as measurement settings at later times). Keeping this time-asymmetric assumption leads to a substantial tension between quantum mechanics and relativity. Relaxing it, as should be considered for such no-go theorems, opens a category of Future-Input Dependent (FID) models, for which this tension need not occur. This option (often called retrocausal’) has been repeatedly pointed out in the literature, but the exploration of explicit FID models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. Unlike conventional quantum models, the FID model parameters needed to specify the state of a system do not grow exponentially with the number of entangled particles. The promise of generalizing FID models into a Lorentz-covariant account of all quantum phenomena is identified as a grand challenge.

# Incorporating action and reaction into a particle interpretation for quantum mechanics — Dirac case

A weakness which has previously seemed unavoidable in particle interpretations of quantum mechanics (such as in the de Broglie-Bohm model) is addressed here and a resolution proposed. The weakness in question is the lack of action and reaction occurring between the model’s field (or “pilot wave”) and the particle. Although the field acts on the particle, the particle does not act back on the field. It is shown here that this rather artificial feature is, in fact, not necessary and can be fully eliminated while remaining consistent with the usual quantum predictions. Mathematically this amounts to demonstrating that there exists a suitable Lagrangian density function which generates equations coinciding with quantum mechanics yet incorporates the desired action and reaction. As a by-product, an appealing possible explanation emerges to another long-standing question, namely why the mathematical formalism of quantum mechanics seems only to be describing fields when measurements generally detect localised particles.

# Quantum gravity from nonnoetherian spacetime

Aristotle proposed that time passes if and only if something changes. We investigate the consequences of incorporating Aristotle’s notion of time into general relativity. We find that the resulting spacetime possesses many quantum-like properties.