Generation and Transformation of Quantum States

W. A. Majewski

Carlo Rovelli C

In classical theory, a physical state is an equivalence class under gauge transformations. Is the same true in quantum theory? The physical quantum states are the solutions of Dirac's quantum constraint equation. They cannot be constructed as equivalence classes under the ``simple'' gauge transformations generated by the Dirac constraints. However, we show here that they can be constructed as equivalence classes under suitably defined ``complete'' gauge transformations. The complete gauge transformations are generated by the action of the quantum constraints on arbitrary individual components of the state.

Sarah Croke, Stephen Mark Barnett, Stig Stenholm

A. Vidiella-Barranco, José Antonio Roversi

We construct a Hamiltonian for the generation of arbitrary pure states of the quantized electromagnetic field. The proposition is based upon the fact that a unitary transformation for the generation of number states has already been found. The general unitary transformation here obtained would allow the use of nonlinear interactions for the production of pure states. We discuss the applicability of this method by giving examples of generation of simple superposition states. We also compare our Hamiltonian with the one resulting from the interaction of trapped ions with two laser fields.

Alon E. Faraggi, Marco Matone

Shun Umekawa, Akihiro Hokkyo, Hayato Arai +1 more

Entanglement generation is a fundamental dynamical capability in quantum information science and underpins many quantum advantages. While quantum theory enables it through unitary dynamics, boxworld, a generalized probabilistic theory admitting Popescu--Rohrlich boxes with supraquantum correlations, has no reversible transformation capable of generating entanglement. We show that this no-go picture changes fundamentally once reversibility is relaxed to pure-state preservation. We construct a pure-state-preserving transformation that maps every uncorrelated pure state to a Popescu--Rohrlich box and completely classify all pure-state-preserving entangling transformations in the simplest bipartite boxworld. Our results provide the first explicit mechanism for generating beyond-quantum entanglement without introducing mixing and demonstrate a physical distinction between reversibility and pure-state preservation that is obscured by the structure of quantum theory.