a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)

Geometry of Quantum States: Frontmatter

https://chaos.if.uj.edu.pl/~karol/erratum10.pdf

Geometry of Quantum States

Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics The acquisition of information from a quantum system is the interface of classical and quantum physics Essential tools for its description are Kraus matrices and positive operator valued measures (POVMs) Special relativity imposes severe restrictions on the transfer of information between distant systems Quantum entropy is not a Lorentz covariant concept Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps Quantum field theory, which is necessary for a consistent description of interactions, implies a fundamental trade-off between detector reliability and localizability General relativity produces new, counterintuitive effects, in particular when black holes (or more generally, event horizons) are involved Most of the current concepts in quantum information theory may then require a reassessment

/pdf/quantum-information-and-relativity-theory-3dkgrtjwvo.pdf

Quantum Information and Relativity Theory

Geometry of quantum states: an introduction to quantum entanglement by Ingemar Bengtsson and Karol Zyczkowski

Developments in the foundations of statistical mechanics during the past ten years or so. The author discusses how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem. Then he deals with large systems: the thermodynamic limit and the theory of infinite systems. Non-equilibrium statistical mechanics is covered but LC relativistic statistical mechanics is not.

https://iopscience.iop.org/article/10.1088/0034-4885/42/12/002/pdf

Foundations of statistical mechanics

The most general dynamical law for a quantum mechanical system with a finite number of levels is formulated. A fundamental role is played by the so-called "dynamical matrix" whose properties are stated in a sequence of theorems. A necessary and sufficient criterion for distinguishing dynamical matrices corresponding to a Hamiltonian time-dependence is formulated. The non-Hamiltonian case is discussed in detail and the application to paramagnetic relaxation is outlined.

Stochastic Dynamics of Quantum-Mechanical Systems

The time variation of the dipole and quadrupole polarizations of a system of spin 1 particles is discussed. The case of axially symmetric external fields is treated in detail and it is shown that this furnishes a canonical representation for the polarization dynamics. Elementary techniques are used to obtain an enumeration of the constants of motion and a geometric representation of the time dependence of the multipole polarizations. (auth)

P. M. Mathews

Papers

Stochastic Dynamics of Quantum-Mechanical Systems

Dynamics of a System of Spin 1 Particles