Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrödinger’s equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born’s rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born’s rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation.
In traditional open quantum systems, the baths are usually traced out so that only the system information is left in the equations of motion. However, recent studies reveal that using only the system degrees of freedom can be insufficient. In this work, we develop a stochastic
c-number Langevin equation method which can conveniently access the bath information. In our approach, the studied quantities are the expectation values of operators which can contain both system operators and bath operators. The dynamics of the operators of interest is formally divided into separate system and bath parts, with auxiliary stochastic fields. After solving the independent stochastic dynamics of the system part and the bath part, we can recombine them by taking the average over these stochastic fields to obtain the desired quantities. Several applications of the theory are highlighted, including the pure dephasing model, the spin-boson model, and an optically excited quantum dot coupled to a bath of phonons.
The purpose of this paper is to develop a model reduction theory for linear quantum stochastic systems that are commonly encountered in quantum optics and related fields, modeling devices such as optical cavities and optical parametric amplifiers, as well as quantum networks composed of such devices. It is shown that subsystem truncation preserves the physical realizability property of linear quantum stochastic systems, and that the property of complete passivity is invariant under subsystem truncation. However, generic linear quantum stochastic systems need not have a balanced realization under symplectic transformations. Therefore, alternative notions of balancing, including so-called quasi-balancing, are developed, and necessary and sufficient conditions are derived. A truncation error bound is derived for quasi-balanceable linear quantum stochastic systems and it is shown that all asymptotically stable completely passive linear quantum stochastic systems have a quasi-balanced realization. An example is provided to illustrate model reduction in the context of low-pass optical filtering of coherent light using a network of optical cavities.