We present the experimental quantum tomography of 7- and 8-dimensional quantum systems based on projective measurements in the mutually unbiased basis (MUB-QT). One of the advantages of MUB-QT is that it requires projections from a minimal number of bases to be performed. In our scheme, the higher dimensional quantum systems are encoded using the propagation modes of single photons, and we take advantage of the capabilities of amplitude- and phase-modulation of programmable spatial light modulators to implement the MUB-QT.

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

We report an interference experiment that shows transverse spatial antibunching of photons. Using collinear parametric down-conversion in a Young-type fourth-order interference setup we show interference patterns that violate classical Schwarz inequality and should not exist at all in a classical description.Photon antibunching in a stationary field is recognized as a signature of nonclassical behavior, for its description is not possible in terms of a nonsingular positive GlauberSudarshan P distribution [1]. It is well known that any state of the electromagnetic field that has a classical analog can be described by means of a positive P distribution which has the properties of a classical probability functional over an ensemble of coherent states.The classical intensity correlation function for stationary fields must obey the following inequality [1]:All field states described in terms of a positive nonsingular P distribution must obey the standard quantum mechanical counterpart of (1), where products of intensities are replaced by ordered products of photon density operators [1], that is,where T : : stands for time and normal ordering. Photon density operators are defined aŝwhereV (r, t) = k,σâ k,σ ǫ k,σ e i(k·r−ωt) , a k,σ is the annihilation operator for the mode with wave vector k and polarization σ, ǫ k,σ is the unit polarization vector, and ω = ck. Inequality (2) means that for such class of fields, photons are detected either bunched or randomly distributed in time. Photon antibunching in time, characterized by the violation of (2) Let us now turn to space domain and consider that the transverse field profile of a given stationary light beam propagating along z direction is described by a complex stochastic vector amplitude V(ρ, t) with an associated probability functional P(V). Here, ρ lies in a plane transverse to the propagation direction. The average intensity at a point ρ isand the two-point intensity correlation functionIts time dependence is restricted to the difference τ = t 1 − t 2 , since the field is assumed to be stationary. In the space domain, the concept analogous to stationarity is homogeneity. For a homogeneous field, the expectation value of any quantity that is a function of position is invariant under translation of the origin [1]. In particular, Γ (2,2) (ρ 1 , ρ 2 , τ ) = Γ (2,2) (δ, τ )andwhere δ = ρ 1 − ρ 2 and N = 1, 2, . . . Applying Schwarz inequality, I(ρ, t)I(ρ + δ, t + τ ) 2 ≤ I 2 (ρ, t) I 2 (ρ + δ, t + τ ) .

Any practical realization of entanglement-based quantum communication must be intrinsically secure and able to span long distances avoiding the need of a straight line between the communicating parties. The violation of Bell’s inequality offers a method for the certification of quantum links without knowing the inner workings of the devices. Energy-time entanglement quantum communication satisfies all these requirements. However, currently there is a fundamental obstacle with the standard configuration adopted: an intrinsic geometrical loophole that can be exploited to break the security of the communication, in addition to other loopholes. Here we show the first experimental Bell violation with energy-time entanglement distributed over 1 km of optical fibres that is free of this geometrical loophole. This is achieved by adopting a new experimental design, and by using an actively stabilized fibre-based long interferometer. Our results represent an important step towards long-distance secure quantum communication in optical fibres.

Side-channel attacks currently constitute the main challenge for quantum key distribution (QKD) to bridge theory with practice. So far two main approaches have been introduced to address this problem, (full) device-independent QKD and measurement-device-independent QKD. Here we present a third solution that might exceed the performance and practicality of the previous two in circumventing detector side-channel attacks, which arguably is the most hazardous part of QKD implementations. Our proposal has, however, one main requirement: the legitimate users of the system need to ensure that their labs do not leak any unwanted information to the outside. The security in the low-loss regime is guaranteed, while in the high-loss regime we already prove its robustness against some eavesdropping strategies.