Armin Tavakoli

Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we introduce and investigate quantum information encoded in carriers that nearly, but not entirely, correspond to standard qudits. We demonstrate the relevance of this concept for semi-device-independent quantum information by showing how small higher-dimensional components can significantly compromise the conclusions of established protocols. Then we provide a general method, based on semidefinite relaxations, for bounding the set of almost qudit correlations, and apply it to remedy the demonstrated issues. This method also offers a novel systematic approach to the well-known task of device-independent tests of classical and quantum dimensions with unentangled devices. Finally, we also consider viewing almost qubit systems as a physical resource available to the experimenter and determine the optimal quantum protocol for the well-known Random Access Code.

Quantum Random Number Generators (QRNGs) are essential components for modern cryptography, as they are a practical source of true randomness, without which the security of such protocols cannot be guaranteed. Among the proposed schemes, Semi-Device-Independent QRNGs (SDI-QRNGs) based on photon-number constraints offer an appealing balance of security, speed, and experimental simplicity, but demonstrations have so far focused mainly on binary encoding and conditional min‑entropy certification. In this work, we report the first experimental implementation of a Continuous‑Variable SDI‑QRNG in a prepare‑and‑measure configuration building on the SDP‑based (Semi-Definite Programming) framework of Ref.~\cite{carceller2025}. This approach allows us to directly lower‑bound the conditional Shannon entropy, employ more complex modulation formats, and apply entropy‑accumulation techniques beyond the i.i.d. assumption. The experiment combines a low-loss integrated photonic heterodyne receiver with a simple transmitter built from commercial components, generating coherent‑state Quadrature-Phase-Shift-Keying (QPSK) modulation, to preserve experimental practicality while enabling high‑speed operation.

Bridging the gap between practical implementation and rigorous security, semi-device-independent quantum key distribution (QKD) offers a compelling middle ground—requiring minimal trust assumptions while achieving key rates competitive with fully characterized protocols. We investigate two conceptually distinct constraints on the preparation device: the information constraint and restricted distrust. We identify protocols that remain secure under both assumptions and demonstrate their robustness to experimental noise. Notably, the widely used BB84 and B92 protocols fail to provide security under the information constraint. To obtain secure key rates, we showcase a numerical framework combining tracial non-commutative polynomial optimization with entropy relaxation techniques. Our approach extends naturally to broader classes of preparation constraints and QKD protocols.