Among the applications of optical phase measurement, the differential interference contrast microscope is widely used for the evaluation of opaque materials or biological tissues. However, the signal to noise ratio for a given light intensity is limi
ted by the standard quantum limit (SQL), which is critical for the measurements where the probe light intensity is limited to avoid damaging the sample. The SQL can only be beaten by using {it N} quantum correlated particles, with an improvement factor of $sqrt{N}$. Here we report the first demonstration of an entanglement-enhanced microscope, which is a confocal-type differential interference contrast microscope where an entangled photon pair ({it N}=2) source is used for illumination. An image of a Q shape carved in relief on the glass surface is obtained with better visibility than with a classical light source. The signal to noise ratio is 1.35$pm$0.12 times better than that limited by the SQL.
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect
small erroneous deviations in reconstructed density matrices, which contain intrinsic fluctuations due to the limited number of samples, than a naive method of checking the trace distance from the average of the given density matrices. This method has the potential to be a key tool in broad areas of physics where the detection of small deviations of quantum states reconstructed using a limited number of samples are essential.
Two path interferometry with coherent states and squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent light. Here, we
investigate the phase sensitivity of such states in the presence of photon losses. It is shown that the Cramer-Rao bound of phase sensitivity can be achieved experimentally by using a weak local oscillator and photon counting in the output. The phase sensitivity is then given by the Fisher information F of the state. In the limit of high squeezing, the ratio (F-N)/N^2 of Fisher information above shot noise to the square of the average photon number N depends only on the average number of photons lost, n_loss, and the fraction of squeezed vacuum photons mu. For mu=1/2, the effect of losses is given by (F-N)/N^2=1/(1+2 n_loss). The possibility of increasing the robustness against losses by lowering the squeezing fraction mu is considered and an optimized result is derived. However, the improvements are rather small, with a maximal improvement by a factor of two at high losses.
It is shown that the addition of down-converted photon pairs to coherent laser light enhances the N-photon phase sensitivity due to the quantum interference between components of the same total photon number. Since most of the photons originate from
the coherent laser light, this method of obtaining non-classical N-photon states is much more efficient than methods based entirely on parametrically down-converted photons. Specifically, it is possible to achieve an optimal phase sensitivity of about delta phi^2=1/N^(3/2), equal to the geometric mean of the standard quantum limit and the Heisenberg limit, when the average number of down-converted photons contributing to the N-photon state approaches (N/2)^(1/2).
We show that the N-photon states produced by interference between laser light and downconverted light at the input of a two path interferometer can be characterized by a single tuning parameter that describes a transition from phase squeezing to near
ly maximal path entanglement and back. The quantum states are visualized on a sphere using the analogy between N-photon interference and the spin-N/2 algebra.
We show that the quantum interference between downconverted photon pairs and photons from coherent laser light can produce a maximally path entangled N-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A si
mple beam splitter operation can thus transform the 2-photon coherence of down-converted light into an almost optimal N-photon coherence.
