Dynamical Correspondence in a Generalized Quantum Theory

Constantin Brif, A. Mann

We present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are (finite-dimensional) Lie groups. The family of distributions on a phase space is postulated to satisfy the Stratonovich - Weyl correspondence with a generalized traciality condition. The corresponding family of the Stratonovich - Weyl kernels is constructed explicitly. In the presented theory we use the concept of generalized coherent states, that brings physical insight into the mathematical formalism.

Asao Arai

DAVID J. ROWE, Moyez G. Vassanji, George Rosensteel

We show that to any Lie algebra of observables in quantum mechanics there corresponds a system of densities, of which the one-body densities are just one example. These densities may correspond to a single pure state or to an ensemble of states. Like the one-body densities, they support a Hamiltonian dynamics of the time-dependent Hartree-Fock type, which can be applied, for example, to collective motions where the collective states of interest may be either more or less general than single Slater determinants. The dynamics can also be applied to the average dynamics of an ensemble of states.

Gerd Niestegge

Kaumudibikash Goswami, Archana Barvar, Manabendra Nath Bera

Quantum states over time were introduced, in part, to extend Bayesian probability to quantum theory and have since found applications across diverse areas, ranging from quantum causality and open-system dynamics to tests of macroscopic realism. While axiomatic characterizations of these states exist for Markovian dynamics, a general framework accommodating non-Markovian dynamics is still lacking. Moreover, extending this framework beyond quantum mechanics to general physical theories also remains elusive. In this work, we develop an axiomatic framework for multi-time states within a class of operational probabilistic theories (OPTs) that includes quantum mechanics as a special case. Based on three assumptions---compositionality, reconstructibility, and spatio-temporal marginal consistency---the framework accommodates both Markovian and non-Markovian dynamics, and provides sufficient conditions to certify signaling and temporal memory within OPT. As a concrete application of our OPT framework, we fully characterize the unique multi-time state in boxworld and develop a method for Bayesian retrodiction of physical transformations there. Our general framework is consistent with quantum theory, reproducing several existing results. In the non-Markovian quantum dynamics, we establish a correspondence between multi-time states and the process-matrix framework, and fully characterize the multi-time states compatible with general dynamics. This correspondence also lets us infer quantum causal models from multi-time states, and as a proof of principle, we propose a semidefinite program to infer causal order from quantum multi-time states. These results provide a unified framework for studying spatio-temporal states, causal relations, and Bayesian reasoning within OPTs, with implications for both fundamental and applied research.

Benno Fuchssteiner