We propose a procedure for tomographic characterization of continuous variable quantum operations which employs homodyne detection and single-mode squeezed probe states with a fixed degree of squeezing and anti-squeezing and a variable displacement a
nd orientation of squeezing ellipse. Density matrix elements of a quantum process matrix in Fock basis can be estimated by averaging well behaved pattern functions over the homodyne data. We show that this approach can be straightforwardly extended to characterization of quantum measurement devices. The probe states can be mixed, which makes the proposed procedure feasible with current technology.
We derive sampling functions for estimation of quantum state fidelity with Schrodinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity with squeezed
Fock states that can approximate the cat-like states and can be generated from Gaussian squeezed states by conditional photon subtraction. The fidelities can be determined by averaging the sampling functions over quadrature statistics measured by homodyne detection. The sampling functions are designed such that they can compensate for losses and inefficient homodyning provided that the overall efficiency exceeds certain threshold. The fidelity with an odd coherent state and the fidelity with a squeezed odd Fock state provide convenient witnesses of negativity of Wigner function of the measured state. The negativity of Wigner function at the origin of phase space is certified if any of these fidelities exceeds 0.5. Finally, we discuss the possibility of reducing the statistical uncertainty of the fidelity estimates by a suitable choice of the dependence of the number of quadrature samples on the relative phase shift between local oscillator and signal beam.
We provide a detailed theoretical analysis of multiple copy purification and distillation protocols for phase diffused squeezed states of light. The standard iterative distillation protocol is generalized to a collective purification of an arbitrary
number of N copies. We also derive a semi-analytical expression for the asymptotic limit of the iterative distillation and purification protocol and discuss its properties.
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible results. Its feasib
ility is demonstrated using the Monte Carlo simulations for the two-level system (single qubit).
