We address estimation of one-parameter qubit gates in the presence of phase diffusion. We evaluate the ultimate quantum limits to precision, seek optimal probes and measurements, and demonstrate an optimal estimation scheme for polarization encoded optical qubits. An adaptive method to achieve optimal estimation in any working regime is also analyzed in detail and experimentally implemented.

The trace distance between two states of an open quantum system quantifies their distinguishability and, for a fixed environmental state, can increase above its initial value only in the presence of initial system-environment correlations. We provide experimental evidence of such a behavior. In our all-optical apparatus, we exploit spontaneous parametric down conversion as a source of polarization entangled states and a spatial light modulator to introduce in a general fashion correlations between the polarization and the momentum degrees of freedom, which act as environment.

Phase diffusion represents a crucial obstacle towards the implementation of high precision interferometric measurements and phase shift based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light.

We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in an effective non-Markovian channel. We generate entangled photon pairs by spontaneous parametric down-conversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization-dependent phase shift on the spatial domain of the SPDC output. This creates an effective programmable non-Markovian environment where modulation of the environment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscillations of entanglement are achieved, where the entangled state obtained at the maximum of the revival after sudden death violates Bell's inequality by 17 standard deviations.

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