Quantum Mechanical Processes

Henry Pierce Stapp

Jen-Hsiang Hsieh, Shih-Hsuan Chen, Che-Ming Li

The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of the natural world, from understanding counter-intuitive concepts to the development of wholly quantum-mechanical technology. Here, we show that quantum-mechanical processes can be quantified using a generic classical-process model through which any classical strategies of mimicry can be ruled out. We demonstrate the success of this formalism using fundamental processes postulated in quantum mechanics, the dynamics of open quantum systems, quantum-information processing, the fusion of entangled photon pairs, and the energy transfer in a photosynthetic pigment-protein complex. Since our framework does not depend on any specifics of the states being processed, it reveals a new class of correlations in the hierarchy between entanglement and Einstein-Podolsky-Rosen steering and paves the way for the elaboration of a generic method for quantifying physical processes.

Martin Pieper

Hermann Grabert, Peter Hänggi A, Peter Talkner A

The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.

Bob Coecke, Aleks Kissinger

Chung-Cheng Kuo, Shih-Hsuan Chen, Wei-Ting Lee +3 more

Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for characterizing and quantifying the ability of processes to cause quantum-mechanical effects on physical systems. We start by introducing a new concept, referred to as quantum process capability, to evaluate the effects of an experimental process upon a prescribed quantum specification. Various methods are then introduced for measuring such a capability. It is shown that the methods are adapted to quantum process tomography for implementation of process capability measure and applicable to all physical processes that can be described using the general theory of quantum operations. The utility of the proposed framework is demonstrated through several examples, including processes of entanglement, coherence, and superposition. The formalism proposed in this study provides a generic approach for the identification of dynamical processes in quantum mechanics and facilitates the general classification of quantum-information processing.