Modewise entanglement of Gaussian states
Alonso Botero and Benni ReznikWe address the decomposition of a multimode pure Gaussian state with respect to a bipartite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single-mode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bipartite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of “isotropic” states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.
It is well known that, despite the misleading imagery conjured by the name, entanglement in a multipartite system cannot be understood in terms of pair-wise entanglement of the parts. Indeed, there are only pairs of systems, but the number of qualitatively distinct types of entanglement scales exponentially in . A good way to think about this is to recognize that a quantum state of a multipartite system is, in terms of parameters, much more akin to a classical probability distribution than a classical state. When we ask about the information stored in a probability distributions, there are lots and lots of “types” of information, and correlations can be much more complex than just knowing all the pairwise correlations. (“It’s not just that A knows something about B, it’s that A knows something about B conditional on a state of C, and that information can only be unlocked by knowing information from either D or E, depending on the state of F…”).
However, Gaussian distributions (both quantum and classical) are described by a number of parameters that grows on quadratically with the number of variables. The pairwise correlations really do tell you everything there is to know about the quantum state or classical distribution. The above paper makes me wonder to what extent we can understand multipartite Gaussian entanglement in terms of pairs of modes. They have shown that this works at a single level, that entanglement across a bipartition can be decomposed into modewise entangled pairs. But since this doesn’t work for mixed states, it’s not clear how to proceed in understanding the remain entanglement within a partition. My intuition is that there is a canonical decomposition of the Gaussian state that, in some sense, lays bare all the multipartite entanglement it has in any possible partitioning, in much the same way that the eigendecomposition of a matrix exposes its the inner workings.
Some reflections are presented on the state of the search for a quantum theory of gravity. I discuss diverse regimes of possible quantum gravitational phenomenon, some well explored, some novel.
A Rigorous Derivation of Electromagnetic Self-force
Samuel E. Gralla, Abraham I. Harte, Robert M. WaldDuring the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle motion" in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density and stress-energy tensor scale to zero size in an asymptotically self-similar manner about a worldline as . In this limit, the charge, , and total mass, , of the body go to zero, and goes to a well defined limit. The Maxwell field is assumed to be the retarded solution associated with plus a homogeneous solution (the "external field") that varies smoothly with . We prove that the worldline γ must be a solution to the Lorentz force equations of motion in the external field . We then obtain self-force, dipole forces, and spin force as first order perturbative corrections to the center of mass motion of the body. We believe that this is the first rigorous derivation of the complete first order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the "reduction of order" procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. There is no corresponding justification for the non-reduced-order equations.
In other words:
…we consider a modified point particle limit, wherein not only the size of the body goes to zero, but its charge and mass also go to zero. More precisely, we will consider a limit where, asymptotically, only the overall scale of the body changes, so, in particular, all quantities scale by their naive dimension. In this limit, the body itself completely disappears, and its electromagnetic self-energy goes to zero.
Inferential vs. Dynamical Conceptions of Physics
David WallaceI contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent’s ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations governing particular degrees of freedom). I contrast these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics; in this last case, I argue that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. Along the way various foundational issues in statistical and quantum physics are (hopefully!) illuminated.
David Wallace is “a physicist’s philosopher” whose work I have recommend highly for a while. In addition to the above article, see “Decoherence and its role in the modern measurement problem” and “What is orthodox quantum mechanics?” for an approach to understanding the measurement problem that strongly accords with, and shaped, my own. On the other hand, I disagree with his defeatist “eh, it’s good enough” assessment of our (currently) messy and hand-wavy way to understand wavefunction branches and think the Set Selection problem is vitally important. I also find Wallace’s justification of the Born rule from decision-theoretic axioms to be fully undermined by Kent’s thorough criticisms.
Separately from quantum mechanics, Wallace’s “The Logic of the Past Hypothesis” is a great discussion of how to think about the thermodynamic justification for, and explanatory content of, asserting a low-entropy state in the past. It greatly changed my opinion on Jayne’s max entropy principle in this context.
Macroscopic quantum states: measures, fragility and implementations
Florian Fröwis, Pavel Sekatski, Wolfgang Dür, Nicolas Gisin, Nicolas SangouardLarge-scale quantum effects have always played an important role in the foundations of quantum theory. With recent experimental progress and the aspiration for quantum enhanced applications, the interest in macroscopic quantum effects has been reinforced. In this review, we critically analyze and discuss measures aiming to quantify various aspects of macroscopic quantumness. We survey recent results on the difficulties and prospects to create, maintain and detect macroscopic quantum states. The role of macroscopic quantum states in foundational questions as well as practical applications is outlined. Finally, we present past and on-going experimental advances aiming to generate and observe macroscopic quantum states.
Observing a breakdown in quantum mechanics is, of course, highly unlikely, but pushing the bounds on the still-only-intuitively-defined notion of “macroscopic” quantum states is among the most promising approaches.Another relatively promising avenue is to explore the limits of contextuality.a To design such experiments and make sure you’re actually doing something new, you want a measure of macroscopicity. This forthcoming RMP contains the most comprehensive summary of measures of macroscopicity that I’ve seen.
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- Links for April-May 2018 (6)
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