Entanglement, separability and correlation topology of quantum systems over parametric space of interaction potential

Abstract

The standard understanding of formal quantum theory is based upon the belief that the state of two interacting quantum systems can jointly evolve as, either an entangled state, e.g. in case of measurement or decoherence, or a separable state, e.g. in case of gate operations, through two different processes, i.e. process-1 and process-2, respectively, as suggested by von Neumann, although nothing much is known about such processes in terms of physical interaction. The present work, exploring the correlation topologies of two interacting quantum systems in parametric space of their interaction potential, reveals that process-1 and process-2 are not different kinds of physical interactions but depend on the interaction parameters to result in either an entangled or a separable state. However, under energy conservation restriction, it is impossible to travel from one maximally-entangled state to another in the topological space by continuously varying such interaction parameters without crossing an intermediate separable state, and vice-versa. Nevertheless, a maximal entangled state is shown to be achieved by violating energy conservation utilizing the energy-time uncertainty or a catalytic separable ancillia. The work explores the nature of interaction potential needed to rotate a qubit state on the entire Bloch sphere, thereby revealing a novel method of measuring the qubit phase avoiding its state-collapse. Further, the manipulation of the degree of non-local entanglement of two space-like apart entangled-qubits in a controlled manner by local unitary operation on one has been illustrated. The generalization of process-1 and process-2 in terms of interaction potential to create entanglement or separability suggests a necessary revisit of the fundamental quantum paradoxes and several other quantum limitations including decoherence for advancing the field of quantum technology as a whole.