Daniele Giovannini

Characterization of High-Dimensional Entangled Systems via Mutually Unbiased Measurements

Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d = 2 to 5.

Determining the dimensionality of bipartite orbital-angular-momentum entanglement using multi-sector phase masks

The Shannon dimensionality of orbital-angular-momentum (OAM) entanglement produced in spontaneous parametric down-conversion can be probed by using multi-sector phase analysers [1]. We demonstrate a spatial light modulator-based implementation of these analysers, and use it to measure a Schmidt number of about 50.

Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems

The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number of generated modes, the number of measured modes is determined by the measurement apparatus. We derive a simple relationship between the generation and detection parameters and the number of measured entangled modes.

Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam

We report orbital angular momentum (OAM) and angle correlations between signal and idler photons observed when the nonlinear crystal used in spontaneous parametric down-conversion is illuminated by a non-fundamental Gaussian pump beam. We introduce a π-phase step to the transverse profile of the pump, before it impinges on the crystal to create a phase-flipped Gaussian mode, which is a close approximation to an HG10 Hermite–Gaussian-like beam. The correlations in OAM and angular position are then measured holographically using two separate spatial light modulators in the signal and idler arms. We show the transfer of the OAM spectrum of the pump to the down-converted fields, manifested as a redistribution in the OAM correlations consistent with OAM conservation. This corresponds to a modulation of the angular position correlations consistent with the Fourier relationship between the OAM and angle.

Photon Orbital Angular Momentum: generation, measurement and application to QKD

The information carried by a photon can be encoded in one or more of many different degrees of freedom. Beyond the two-dimensional space of polarisation (spin angular momentum) our interest lies in the unbounded yet discrete state space of Orbital Angular Momentum (OAM). We examine how photon pairs can be generated and measured over a large range of OAM states.

Encoding mutually unbiased bases in orbital angular momentum for quantum key distribution

We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform (d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.

Interference of probability amplitudes: a simple demonstration within the Hong-Ou-Mandel experiment

The dip in the Hong–Ou–Mandel (HOM) experiment is frequently attributed to the interference of two indistinguishable photons. The width of the dip is inversely proportional to the spectral bandwidth of the light. We confirm that this width is unchanged regardless of where the bandwidth selection happens, i.e. prior to the photons combining in the beam splitter or just before the detectors; the latter case seemingly after the interference of the photons. The equivalence of the results from these two cases is a simple demonstration that the interference in the HOM experiment is not between photons, but rather between probability amplitudes.

Maximizing the Dimensionality of Orbital Angular Momentum Entanglement in Parametric Down-conversion

Parametric down-conversion is a source of high-dimensional states entangled in orbital angular momentum (OAM). We analyze and maximize the number of OAM modes produced by down-conversion and detected by our measurement apparatus.

Increasing the orbital angular momentum bandwidth of entangled photons

The bandwidth of any communication system, classical or quantum, is limited by the number of orthogonal states in which the information can be encoded. Quantum key distribution systems available commercially rely on the two-dimensional polarisation state of photons. Quantum computation has also been largely designed on the basis of qubits. However, a photon is endowed with other degrees of freedom, such as orbital angular momentum (OAM). OAM is an attractive basis to be used for quantum information because it is discrete and theoretically infinite-dimensional. This promises a higher information capacity per photon which can lead to more complex quantum computation protocols and more security and robustness for quantum cryptography. Entanglement of OAM naturally arises from spontaneous parametric down-conversion (SPDC). However, any practical experiment utilising the innately high-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. Only a finite subset of this space is accessible experimentally. Given such a constraint, we show that the number of measured, entangled OAM modes in photon pairs generated by SPDC can be increased by tuning the phase-matching conditions in the SPDC process. We achieve this by tuning the orientation angle of the nonlinear crystal generating the entangled photons.