# Weekly Papers on Quantum Foundations (41)

Quantum measurement incompatibility in subspaces. (arXiv:2010.04048v1 [quant-ph])

We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.

Quantum Zeno effect for open quantum systems. (arXiv:2010.04121v1 [quant-ph])

We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.

Revisiting the experimental test of Mermin’s inequalities at IBMQ. (arXiv:2005.11271v2 [quant-ph] UPDATED)

Bell-type inequalities allow for experimental testing of local hidden variable theories. In the present work we show the violation of Mermin’s inequalities in IBM’s five-qubit quantum computers, ruling out the local realism hypothesis in quantum mechanics. Furthermore, our numerical results show significant improvement with respect to previous implementations. The circuit implementation of these inequalities is also proposed as a way of assessing the reliability of different quantum computers.

Does locality plus perfect correlation imply determinism?. (arXiv:2009.14223v1 [quant-ph] CROSS LISTED)

Authors: Michael J.W. Hall

A 1964 paper by John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. There is an ongoing and vigorous debate on whether he relied on an assumption of determinism, or instead, as he later claimed, derived determinism from assumptions of locality and perfect correlation. This paper aims to bring clarity to the debate via simple examples and rigorous results. It is shown that the weak form of locality used in Bell’s 1964 paper (parameter independence) is insufficient for such a derivation, whereas an independent form called outcome independence is sufficient even when weak locality does not hold. It further follows that outcome independence, by itself, implies that standard quantum mechanics is incomplete. It is also shown that an appeal by Bell to the Einstein-Rosen-Podolsky argument to support his claim fails, via examples that expose logical gaps in this argument. However, replacing the reality criterion underpinning the argument by a stronger criterion enables a rigorous derivation of both weak locality and determinism, as required for Bell’s 1964 paper. Consequences for quantum interpretations, locality, and classical common causes are briefly discussed, with reference to an example of local classical indeterminism.

Exponential corrected thermodynamics of black holes. (arXiv:2010.03946v1 [gr-qc])

Authors: Behnam Pourhassan

Recently, it is reported that thermal fluctuations which are interpreted as quantum effects, modify black holes entropy by an exponential term. We now find the effect of such modification on black hole mass and other thermodynamics quantities. We find that Schwarzschild black hole mass decreased by thermal fluctuations. Hence, we study exponential corrected thermodynamics and statistics of black holes by computing the partition function. We obtain special condition on the event horizon radius to satisfy Smarr-Gibbs-Duhem relation in the presence of quantum correction. As we know the Schwarzschild black hole is unstable, while the effect of exponential correction is the stability of $4D$ Schwarzschild black hole as well as the Schwarzschild-AdS black hole at a small area. On the other hand, a $5D$ Schwarzschild black hole is completely unstable. The effect of quantum correction on the Reissner-Nordstr\”{o}m black hole is instability at quantum scales. Finally, we consider the most general case of charged AdS black hole and study corrected thermodynamics.

How to form a wormhole. (arXiv:2010.03947v1 [gr-qc])

Authors: De-Chang DaiDjordje MinicDejan Stojkovic

We provide a simple but very useful description of the process of wormhole formation. We place two massive objects in two parallel universes (modeled by two branes). Gravitational attraction between the objects competes with the resistance coming from the brane tension. For sufficiently strong attraction, the branes are deformed, objects touch and a wormhole is formed. Our calculations show that more massive and compact objects are more likely to fulfill the conditions for wormhole formation. This implies that we should be looking for wormholes either in the background of black holes and compact stars, or massive microscopic relics. Our formation mechanism applies equally well for a wormhole connecting two objects in the same universe.

Relativistic generalization of the Schrodinger-Newton model for the wavefunction reduction. (arXiv:2010.03971v1 [gr-qc])

We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of the Schrodinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the “active” gravitational masses are always positive, and approximately equal to inertial masses and to the mass $m$ of the quanta of Dirac field up to the corrections of order $\alpha^2$. Here $\alpha=(m/M_{pl})^2$ is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit $\alpha \to 0$ the model reduces back to the nonrelativistic Schrodinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is $\alpha$ times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process

A Unified Combination of Classical and Quantum Systems. (arXiv:2010.03984v1 [quant-ph])

Authors: John R. Klauder

Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a clear and continuous passage between the conventional distinction of either a strictly classical or a strictly quantized state. While path integration, among other procedures, provides an alternative route to connect classical and quantum expressions, it normally involves complicated, model-dependent, integrations. Our alternative procedures involve only model-independent procedures, and use more natural and straightforward integrations that are universal in kind. To introduce the basic procedures our presentation begins with familiar methods that are limited to basic, conventional, canonical quantum mechanical examples. In the final sections we illustrate how alternative quantization procedures, e.g., spin and affine quantizations, can also have smooth paths between classical and quantum stories, and with a few brief remarks, can also lead to similar stories for non-renormalizable covariant scalar fields as well as quantum gravity.

Reply to “Comment on “Cosmic Microwave Background Constraints Cast a Shadow On Continuous Spontaneous Localization Models””. (arXiv:2010.04067v1 [gr-qc])

Authors: Jerome MartinVincent Vennin

Our recent letter “Cosmic Microwave Background Constraints Cast a Shadow On Continuous Spontaneous Localization Models” has recently been criticised in [G. R. Bengochea, G. Leon, P. Pearle, and D. Sudarsky, arXiv:2006.05313 and arXiv:2008.05285]. In this reply, we explain why the arguments presented in those articles are either incorrect or a confirmation of the robustness of our results.

Flow: the Axiom of Choice is independent from the Partition Principle

Sant’Anna, Adonai and Bueno, Otávio and de França, Márcio and Brodzinski, Renato (2020) Flow: the Axiom of Choice is independent from the Partition Principle. [Preprint]

The physical limits of computation inspire an open problem that concerns abstract computable sets X⊆N and cannot be formalized in the set theory ZFC as it refers to our current knowledge on X

Kurpaska, Sławomir and Tyszka, Apoloniusz (2020) The physical limits of computation inspire an open problem that concerns abstract computable sets X⊆N and cannot be formalized in the set theory ZFC as it refers to our current knowledge on X. [Preprint]

Coming to America: Carnap, Reichenbach and the Great Intellectual Migration. Part I: Rudolf Carnap

Verhaegh, Sander (2020) Coming to America: Carnap, Reichenbach and the Great Intellectual Migration. Part I: Rudolf Carnap. [Preprint]

Implementing David Lewis’ Principal Principle: A Program for Investigating the Relation between Credence and Chance

John, S (2020) Implementing David Lewis’ Principal Principle: A Program for Investigating the Relation between Credence and Chance. [Preprint]

Intercontinental comparison of optical atomic clocks through very long baseline interferometry

Nature Physics, Published online: 05 October 2020; doi:10.1038/s41567-020-01038-6

Very long baseline interferometry is used to compare two optical clocks located in Japan and Italy through the observation of extragalactic radio sources. This approach overcomes limitations of the performance of satellite transfer techniques.

Chaotic worms

Nature Physics, Published online: 05 October 2020; doi:10.1038/s41567-020-01058-2

Animals seem capable of an infinite variety of movement, yet also exhibit substantial stereotypy in repeated actions. A beautiful view of worm behaviour now shows that the worm’s state evolves deterministically but is bounced chaotically between unstable periodic orbits.