Savarese, Paola (2025) QUANTUM INFORMATION PROCESSING VIA SPIN-ORBIT PHOTONICS. [Tesi di dottorato]

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Abstract

Information is a fundamental concept in both science and technology. From everyday communication to modern computation, the capability to encode, transmit, and process information has become an essential element of our modern society. The mathematical theory of information, introduced by Shannon in 1948, provided the framework to quantify and optimize the storage and transmission of classical data. Within this framework, quantities such as entropy and channel capacity emerge as fundamental measures, setting the bounds on how information can be manipulated through a physical channel. With the advent of quantum mechanics, the unit of information itself was redefined. The quantum bit, or qubit, defines a two-level system that can exist in a superposition of logical states, and entangled pairs of qubits display correlations stronger than any classical one. Yet, quantum information is not intrinsically limited to two levels, and by exploiting either a single high-dimensional degree of freedom (DoF) or multiple DoFs, one can access higher-dimensional Hilbert spaces and encode information in qudits. The dimensionality of these spaces acts as a genuine resource, enabling richer encodings, enhanced robustness to noise, and novel applications in computation, simulation, and communication. However, the manipulation of qudits requires dedicated quantum platforms. Among the available platforms, light offers unique advantage. In fact, it propagates at high speed, is resilient to decoherence, and can be engineered to access multiple tunable DoFs, including polarization, spatial distribution, and temporal modes. Within the paraxial approximation, light can be structured in the transverse plane of propagation, giving rise to a wide variety of patterns, and by acting on its DoFs, structured light provides a versatile tool to encode and process information in very large Hilbert spaces, making it a powerful instrument for exploring quantum information theory. It therefore becomes essential to develop devices capable of reliably manipulating these DoFs. This work investigates nematic liquid crystal (LC) metasurfaces as a powerful method to manipulate the information encoded into optical DoFs. These devices can be engineered to provide full control over the polarization and spatial modes of light. The orientation of LCs along the propagation axis governs the phase retardation, and their orientation in the transverse plane enables spin-orbit coupling, linking the vectorial (polarization) and orbital (spatial) DoFs of light, and introducing a Pancharatnam-Berry geometric phase contribution to the modes of light. In this thesis, two main device families are investigated. The first is that of dichroic LC devices that combine birefringence with dichroism induced by dye molecules aligned with LCs. This configuration introduces tunable polarization dependent losses that implement non-unitary (n-U) transformations. These devices are employed to realize n-U quantum walk (QW) dynamics, where the ballistic spreading of the walk is preserved despite the presence of dissipation, in contrast to its classical counterpart. The distinctive advantage of this scheme is the precise electrical control of polarization, phase and amplitude, which enables systematic exploration of different dynamical regimes. This capability makes this platform well suited for controlled simulation of open quantum systems and for the investigation of non-Hermitian models relevant to photonic topology, where novel physical effects and unconventional topological classes emerge. Conversely, birefringent LC based polarization masks impose spatially localized transformations on propagating modes of light, enabling control over the position and momentum bases. Combined with generalized beam splitters, these devices are used to realize arbitrary unitary transformations in SU(4), extending Zeilinger’s scheme of a universal interferometer towards spin dependent generalized operations. The distinctive advantage of this scheme is the ability to address different spatial modes in parallel while maintaining coherent control of light, allowing for flexible reconfiguration. This capability makes these devices particularly suited for the realization of generalized logic gates in higher-dimensional Hilbert spaces, providing a pathway towards scalable implementations of photonic quantum computing.

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