Entanglement of two-mode Schrodinger cats
Résumé
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous ``Schrodinger cat'' state. The recent progress shows an increase in the number of components and the number of modes involved. Our work gives a theoretical treatment of multicomponent two-mode Schrodinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. After performing a symmetric (Lowdin) orthogonalization of the sets of coherent states in both modes we obtain the Schmidt decomposition of the two-mode state, and therefore an analytic expression for its entanglement. We show that the states obtained by splitting a RICS are generalizations of Bell states of two qubits to the case of N-level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that an exact probabilistic teleportation of arbitrary superposition of coherent states on the circle is possible with such a state used as shared resource.