Abstract. We address joint photodetection as a method to discriminate between the classical correlations of a thermal beam divided by a beam splitter and the quantum entanglement of a twin-beam obtained by parametric downconversion. We show that for intense beams of light the detection of the difference photocurrent may be used, in principle, in order to reveal entanglement, while the simple measurement of the correlation coefficient is not sufficient. We have experimentally measured the correlation coefficient and the variance of the difference photocurrent on several classical and quantum states. Results are in good agreement with theoretical predictions taking into account the extra noise in the generated fields that is due to the pump-laser fluctuations.

We give a simple multiround strategy that permits to beat the shot noise limit when performing interferometric measurements even in the presence of loss. In terms of the average photon number employed, our procedure can achieve twice the sensitivity of conventional interferometric ones in the noiseless case. In addition, it is more precise than the (recently proposed) optimal two-mode strategy even in the presence of loss.PACS numbers: 03.65. Ta,06.20.Dk,42.50.St The shot noise limit is the minimum noise level that the Heisenberg uncertainty relations permit to achieve when classical states are employed in the apparatuses. Many quantum strategies have been proposed to beat the shot noise [1,2] and to achieve the ultimate Heisenberg limit [12], but virtually all of them are very sensitive to noise and loss of photons [3]. Only very recently some interferometric strategies were presented that can beat the shot noise even in the presence of relevant losses of photons [4,5]. These are all instances of parallel strategies [2], where both arms of the interferometer are sampled at the same time using a mode-entangled quantum state of the light (see Fig. 1a). In addition to the parallel strategies, in quantum metrology it is also possible to achieve the Heisenberg limit using multiround (or sequential) strategies [6,7] which, in the noiseless case, are equivalent in terms of resources and of achievable precision [2]. Both arms of the interferometer are sampled at the same time using a two-mode entangled state. The phase factor ϕ is imprinted in the state as a phase difference between the two modes. b) Sequential strategy proposed here. A loss-resistant single mode state is sent through the first interferometer arm, sampling the phase ϕ. Then a unitary transformation is applied and the state is sent back through the other interferometer arm. This is needed so that the final phase shift experienced by the state is only the relative phase in the interferometer. The state is measured after one (or more) round trips.Here we detail how multiround strategies can be used to perform interferometry-see Fig. 1b. An appropriate input state is prepared (we will analyze two examples below). This state is fed into the first interferometer arm. It picks up a phase ϕ + ϑ, where ϕ is the interferometric phase we want to estimate, and ϑ is the absolute phase picked up by the free evolution in the arm (which is equal to the phase which would be picked up also in the reference arm). The main trick of multiround interferometry is the use of the unitarywhere |n is the Fock basis and M is the largest nonzero component of the initial input state. The purpose of this unitary is to permute the first M components of the Fock state expansion of a state in such a way that, when the state is sent back through the reference arm, the absolute phase ϑ is removed from the state (only an irrelevant global phase factor e iMϑ persists). Thus, at the end of the round trip of Fig. 1b (multiple round trips are also possible), only the relative phase ϕ is im...

We address potential deviations of radiation field from the bosonic behaviour and employ local quantum estimation theory to evaluate the ultimate bounds to precision in the estimation of these deviations using quantum-limited measurements on optical signals. We consider different classes of boson deformation and found that intensity measurement on coherent or thermal states would be suitable for their detection making, at least in principle, tests of boson deformation feasible with current quantum optical technology. On the other hand, we found that the quantum signal-to-noise ratio (QSNR) is vanishing with the deformation itself for all the considered classes of deformations and probe signals, thus making any estimation procedure of photon deformation inherently inefficient. A partial way out is provided by the polynomial dependence of the QSNR on the average number of photon, which suggests that, in principle, it would be possible to detect deformation by intensity measurements on high-energy thermal states.Comment: 9 page