We demonstrate qudit encoding in the spectrum of energy-time entangled photons by means of pulse shaping techniques known from ultra-fast laser physics. Quantum state tomography up to d = 4 and Bell test measurements are performed.
Entanglement is a key feature of quantum mechanics and is best suited to study the peculiar nature of non-classical correlations. Higher dimensional entangled bipartite systems beyond qubits allow for new insights in generalized Bell inequalities and for enhanced bit rates within protocols for quantum key distribution. Entangled qutrits and ququarts in the time domain have been implemented interferometrically. This paper proposes and demonstrates the capability to encode qudits in the spectrum of energy-time entangled photons by means of spectral amplitude and phase modulation.
We demonstrate the creation, characterization, and manipulation of frequency-entangled qudits by shaping the energy spectrum of entangled photons. The generation of maximally entangled qudit states is verified up to dimension d=4 through tomographic quantum-state reconstruction. Subsequently, we measure Bell parameters for qubits and qutrits as a function of their degree of entanglement. In agreement with theoretical predictions, we observe that for qutrits the Bell parameter is less sensitive to a varying degree of entanglement than for qubits. For frequency-entangled photons, the dimensionality of a qudit is ultimately limited by the bandwidth of the pump laser and can be on the order of a few millions.
We present a setup for quantum cryptography based on photon pairs in energy-time Bell states and show its feasibility in a laboratory experiment. Our scheme combines the advantages of using photon pairs instead of faint laser pulses and the possibility to preserve energy-time entanglement over long distances. Moreover, using four-dimensional energy-time states, no fast random change of bases is required in our setup: Nature itself decides whether to measure in the energy or in the time base, thus rendering eavesdropper attacks based on "photon number splitting" less efficient.