Pentagrams and paradoxes (2009)
Badziag, Piotr, Bengtsson, Ingemar, Cabello, Adan, Granstrom, Helena, Larsson, Jan-Ake
Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert...
All Mutually Unbiased Bases in Dimensions Two to Five (2009)
Brierley, Stephen, Weigert, Stefan, Bengtsson, Ingemar
All complex Hadamard matrices in dimensions two to five are known. We use this fact to derive all inequivalent sets of mutually unbiased (MU) bases in low dimensions. We find a three-parameter family...
gr-qc/yymmnnn Degenerate Metric Phase Boundaries (2009)
The Erwin, Schrödinger International Boltzmanngasse, Ingemar Bengtsson, Ted Jacobson, Ingemar Bengtsson, Ted Jacobson
The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar’s canonical reformulation of Einstein’s equations is studied. Several examples are given of such “phase...
`Classical' quantum states (2009)
Kuś, Marek, Bengtsson, Ingemar
We show that several classes of mixed quantum states in finite-dimensional Hilbert spaces which can be characterized as being, in some respect, 'most classical' can be described and analyzed in a...
A Note on trapped Surfaces in the Vaidya Solution (2008)
Bengtsson, Ingemar, Senovilla, José M. M.
The Vaidya solution describes the gravitational collapse of a finite shell of incoherent radiation falling into flat spacetime and giving rise to a Schwarzschild black hole. There has been a question...
State-independent violation of correlation inequalities for non-contextual theories (2008)
Badziag, Piotr, Bengtsson, Ingemar, Cabello, Adan, Pitowsky, Itamar
We show that for any physical system of dimension $d \ge 3$, any non-contextual theory satisfies some inequalities for the correlations of compatible measurements which are violated by quantum...
The Frame Potential, on Average (2008)
Bengtsson, Ingemar, Granstrom, Helena
A SIC consists of N^2 equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N^2 unit vectors. It has a unique global minimum if the vectors form a SIC, and...
An Introduction to Quantum Entanglement (2008)
Ingemar Bengtsson, Karol Zyczkowski
[1] S. Abe. A note on the q-deformation-theoretic aspect of the
Anti-de Sitter Quotients, Bubbles of Nothing, and Black Holes (2008)
Aman, Jan E., Aminneborg, Stefan, Bengtsson, Ingemar, Pidokrajt, Narit
In 3+1 dimensions there are anti-de quotients which are black holes with toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de Sitter solution (and appropriate...
Anti-de Sitter Quotients: When Are They Black Holes? (2008)
Aminneborg, Stefan, Bengtsson, Ingemar
We point out that the BTZ black holes, and their relatives, can be defined in a cleaner way than they originally were. The covering space can be taken to be anti-de Sitter space, period, while scri...
Degenerate Metric Phase Boundaries (2007)
Ingemar Bengtsson Fysikum, Ingemar Bengtsson, Ted Jacobson
The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such...
BLACK HOLES AND WORMHOLES IN 2+1 DIMENSIONS (2007)
Ingemar Bengtsson, Dieter Brill, Soren Holst
A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider...
Spectra of phase point operators in odd prime dimensions and the extended Clifford group (2007)
Appleby, D. M., Bengtsson, Ingemar, Chaturvedi, S.
We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete...
A Curious Geometrical Fact About Entanglement (2007)
I sketch how the set of pure quantum states forms a phase space, and then point out a curiousity concerning maximally entangled pure states: they form a minimal Lagrangian submanifold of the set of...
Note on non-metric gravity (2007)
We discuss a class of alternative gravity theories that are specific to four dimensions, do not introduce new degrees of freedom, and come with a physical motivation. In particular we sketch their...
Three ways to look at mutually unbiased bases (2006)
This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent...
Mubs and Hadamards of Order Six (2006)
Bengtsson, Ingemar, Bruzda, Wojciech, Ericsson, Asa, Larsson, Jan-Ake, Tadej, Wojciech, Zyczkowski, Karol
We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the...
An Introduction to Quantum Entanglement: a Geometric Approach (2006)
Zyczkowski, Karol, Bengtsson, Ingemar
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of...
Flat Information Geometries in Black Hole Thermodynamics (2006)
Aman, J. E., Bengtsson, Ingemar, Pidokrajt, Narit
The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or...
Anti-de Sitter space, squashed and stretched (2005)
Bengtsson, Ingemar, Sandin, Patrik
We study the Lorentzian analogues of the squashed 3-sphere, namely 2+1 dimensional anti-de Sitter space, squashed or stretched along fibres that are either spacelike or timelike. The causal...
Geometrical Statistics--Classical and Quantum (2005)
This is a review of the ideas behind the Fisher--Rao metric on classical probability distributions, and how they generalize to metrics on density matrices. As is well known, the unique Fisher--Rao...
On the structure of the body of states with positive partial transpose (2005)
Szarek, Stanislaw, Bengtsson, Ingemar, Zyczkowski, Karol
We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2...
Mutually Unbiased Bases and The Complementarity Polytope (2004)
Bengtsson, Ingemar, Ericsson, Asa
A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a geometrical object such a polytope exists for...
MUBs, polytopes, and finite geometries (2004)
A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p^k, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist...
The Importance of Being Unistochastic (2004)
A bistochastic matrix is a square matrix with positive entries such that rows and columns sum to unity. A unistochastic matrix is a bistochastic matrix whose matrix elements are the absolute values...
Birkhoff's polytope and unistochastic matrices, N=3 and N=4 (2004)
Bengtsson, Ingemar, Ericsson, Asa, Kus, Marek, Tadej, Wojciech, Zyczkowski, Karol
The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic...
On duality between quantum maps and quantum states (2004)
Zyczkowski, Karol, Bengtsson, Ingemar
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A...
Central bank power: a matter of coordination rather than money supply (2003)
After an introductory chapter, the hypothesis is made in chapter two: that central bank power to control the rate of inflation rests on the bankâs ability to achieve a role as a focal point for...
Geometry of black hole thermodynamics (2003)
Aman, Jan, Bengtsson, Ingemar, Pidokrajt, Narit
The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of...
How to mix a density matrix (2002)
Bengtsson, Ingemar, Ericsson, Asa
A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize...
Relativity of pure states entanglement (2001)
Zyczkowski, Karol, Bengtsson, Ingemar
Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of...
2+1 gravity, chaos and time machines (2000)
Bengtsson, Ingemar, Braennlund, Johan
2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian....
A note on topological brane theories (2000)
Bengtsson, Ingemar, Sa, Nuno Barros E, Zabzine, Maxim
We consider the theory of closed $p$-branes propagating on $(p+1)$-dimensional space-time manifolds. This theory has no local degrees of freedom. Here we study its canonical and BRST structures of...
De Sitter Space and Spatial Topology (1999)
Bengtsson, Ingemar, Holst, Soeren
Morrow-Jones and Witt have shown that generic spatial topologies admit initial data that evolve to locally de Sitter spacetimes under Einstein's equations. We simplify their arguments, make them a...
A Spinning Anti-de Sitter Wormhole (1998)
Aminneborg, Stefan, Bengtsson, Ingemar, Holst, Soren
We construct a 2+1 dimensional spacetime of constant curvature whose spatial topology is that of a torus with one asymptotic region attached. It is also a black hole whose event horizon spins with...
Black Holes and Wormholes in 2+1 Dimensions (1997)
Aminneborg, Stefan, Bengtsson, Ingemar, Brill, Dieter, Holst, Soren, Peldan, Peter
A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider...
Degenerate Metric Phase Boundaries (1997)
Bengtsson, Ingemar, Jacobson, Ted
The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such "phase...
Black Holes And Wormholes In 2+1 Dimensions (1997)
Stefan Aminneborg, Ingemar Bengtsson, Dieter Brill, Sören Holst, Peter Peldán, Norra Reals
A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider...
Manifest Duality in Born-Infeld Theory (1996)
Born-Infeld theory is formulated using an infinite set of gauge fields, along the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is generated by a fully local functional....
Bengtsson, Ingemar, Kleppe, Astri
Some aspects of chiral p-forms, in particular the obstruction that makes it hard to define covariant Green functions, are discussed. It is shown that a proposed resolution involving an infinite set...
Making Anti-de Sitter Black Holes (1996)
Aminneborg, Stefan, Bengtsson, Ingemar, Holst, Soren, Peldan, Peter
It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable...
Neighbours of Einstein's Equations: Connections and Curvatures (1995)
Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of...
Form Geometry and the 'tHooft-Plebanski Action (1995)
Riemannian geometry in four dimensions, including Einstein's equations, can be described by means of a connection that annihilates a triad of two-forms (rather than a tetrad of vector fields). Our...
Note on Massive Spin 2 in Curved Space (1994)
We give a Hamiltonian formulation of massive spin 2 theory in arbitrary Einstein space-times. We pay particular attention to Higuchi's forbidden mass range in deSitter space.
Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection,...
Clifford Algebra of Two-Forms, Conformal Structures and Field Equations (1992)
I review the equivalence between duality operators on two-forms and conformal structures in four dimensions, from a Clifford algebra point of view (due to Urbantke and Harnett). I also review an...
Adventures on the light front /--by Ingemar Bengtsson. (1984)
Thesis (doctoral)--Chalmers tekniska högskola, 1984.
A framework for understanding inflation - with or without money
This paper presents a model that pictures how inflation is determined in a decentralized market process where prices are set in both simultaneous and sequential contracts. Price setting is seen as a...
Transaction Costs, Money and Units of Account
In the paper, an analogy with length measurement is applied in order to explore the nature of the unit for value measurement, i.e. the unit of account. As the meter is defined as the length traveled...
TRANSACTION COSTS, MONEY AND UNITS OF ACCOUNT
In this paper, an analogy with length measurement is applied in order to explore the nature of the unit for value measurement, i.e., the unit of account. As the meter is defined as the length...
Central Bank Power is a Matter of Faith
This paper reconsiders how central banks involve itself in the process of determining nominal variables such as market interest rates and inflation rates. Here, it is argued that the traditional...
Central bank power is a matter of faith
This paper reconsiders how central banks get involved in the process of determining nominal variables such as market interest rates and inflation rates. It is argued that the traditional story...
Making Anti-De Sitter Black Holes
Stefan Aminneborg, Ingemar Bengtsson, Soren Holst, Peter Peld'an
It is known from the work of Ba~nados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a...