Do the Boson transformations generate classical states

Reinhard Honegger, Alfred Rieckers

Hong-Yi Fan, Yue Fan

We show that the generalized bosonic Bogolyubov transformation generator [Formula: see text] where G is a n×n matrix, has the manifest coherent state representation [Formula: see text] This expression has the advantage of exhibiting the transition from classical transformation to its quantum mechanical correspondence apparent and providing us with a convenient approach for calculating some Bogolyubov transformed states.

Anil Roy

Fan Hong‐Yi

The formalism of mapping a classical canonical transformation to quantum unitary operators for a boson system is generalized to fermion systems. In terms of the ``integration within an ordered product'' technique for fermion systems, the transition of a classical transformation in Grassmann number space to a quantum image is manifestly evaluated in the fermion coherent-state representation. The normally ordered unitary operators that generate the Bogolyubov-Valatin transformation and the SU(2) rotation are derived in this way.

Bing He, János A. Bergou

We present an optimal scheme to realize the transformations between single copies of two bipartite entangled states without classical communication between the sharing parties. The scheme achieves the upper bound for the success probabilities [Phys. Rev. A 63, 022301 (2001); Phys. Rev. Lett. 83, 1455 (1999)] of generating maximally entangled states if applied to entanglement concentration. Such a strategy also dispenses with the interaction with an ancilla system in the implementation. We also show that classical communications are indispensable in realizing the deterministic transformations of a single bipartite entangled state. With a finite number of identical pairs of two entangled bosons, on the other hand, we can realize the deterministic transformation to any target entangled state of equal or less Schmidt rank through an extension of the scheme.

J. DOBACZEWSKl, Jan Dobeš, H. B. Geyer +3 more