Related papers: Weak* decomposition and Radon-Nikodym theorem for …
Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally…
We show that Lance's weak expectation property is connected to tight Riesz interpolations in lattice theory. More precisely we first prove that if A \subset B(H) is a unital C*-subalgebra, where B(H) is the bounded linear operators on a…
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one,…
We prove Khintchine type inequalities for words of a fixed length in a reduced free product of $C^*$-algebras (or von Neumann algebras). These inequalities imply that the natural projection from a reduced free product onto the subspace…
Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) - S(\rho_C)\geq 0$ for any tripartite density matrix $\rho_{ABC}$, a fact that is equivalent to the…
In this paper, we prove that if $\mathcal{A}$ is a unital separable $C^*$-algebra, $\mathcal{M}$ is a von Neumann algebra which has the Kirchberg's quotient weak expectation property (QWEP), and $\phi:\, \mathcal{A}\rightarrow \mathcal{M}$…
For an ergodic system, the time average of a classical observable coincides with that obtained via the Liouville probability density, a delta-function on the energy shell. Reinterpreting this distribution as a Wigner function, that is, the…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
We show that in the space of nuclear operators from $\ell^q(\Lambda)$ to $\ell^p(J)$ the two natural ways of measuring weak non-compactness coincide. We also provide explicit formulas for these measures. As a consequence the same is proved…
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…
A classic theorem of T. Ando characterises operators that have numerical radius at most one as operators that admit a certain positive 2x2 operator matrix completion. In this paper we consider variants of Ando's theorem, in which the…
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM…
Unlike the real part of the generalized weak value of an observable, which can in a restricted sense be operationally interpreted as an idealized conditioned average of that observable in the limit of zero measurement disturbance, the…
We limit ourselves basically to the SU(2) flavor sector of the CKM matrix, as probed in processes like nuclear $\beta$-decay, normal and radiative muon capture and neutrino reactions. Current interests in this primarily stem from our…
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…