Quantum contracts between Schrödinger and a cat

Lorenza Viola, Roberto Onofrio

Contractive states for a free quantum particle were introduced by Yuen (Yuen H P 1983 Phys. Rev. Lett. 51 719) in an attempt to evade the standard quantum limit for repeated position measurements. We show how appropriate families of two- and three-component `Schrödinger cat states' are able to support non-trivial correlations between the position and momentum observables leading to contractive behaviour. The existence of contractive Schrödinger cat states is suggestive of potential novel roles of non-classical states for precision measurement schemes.

Jeffrey Bub

Marco G. Genoni, Tommaso Tufarelli

Abstract Many quantum statistical models are most conveniently formulated in terms of non-orthogonal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the analytical evaluation of the quantum Fisher information matrix may be greatly simplified by avoiding both the diagonalization of the density matrix and the orthogonalization of the basis. The key ingredient in our method is the Gramian matrix (i.e. the matrix of scalar products between basis elements), which may be interpreted as a metric tensor for index contraction. As an application, we derive novel analytical results for several estimation problems involving noisy Schrödinger cat states.

Edward B. Manoukian

Krzysztof Wódkiewicz

The nonlocality of the Schrödinger cat is established. A correlation measurement that exhibits quantum interference in the form of the Wigner function of the cat state is introduced. The relation of this correlation to quantum interference in phase space and the nonlocal character of the Schrödinger cat are discussed. It is shown that the Schrödinger cat correlation function leads to violation of the Bell inequality for macroscopically distinguishable states of the cat.

Charles S. Adams