Harnessing hybrid frequency-entangled qudits through quantum interference

High-dimensional (HD) quantum entanglement expands the Hilbert space, offering a robust framework for quantum information processing with enhanced capacity and error resilience. In this work, we present an HD frequency-domain entangled state, the hybrid frequency-entangled qudit (HFEQ), generated via Hong-Ou-Mandel (HOM) interference, exhibiting both discrete-variable (DV) and continuous-variable (CV) characteristics in the frequency domain. By tuning HOM interference, we generate and control HFEQs with dimensions <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>D</a:mi> <a:mo>=</a:mo> <a:mn>5</a:mn> <a:mo>,</a:mo> <a:mn>7</a:mn> <a:mo>,</a:mo> <a:mn>9</a:mn> <a:mo>,</a:mo> </a:mrow> </a:math> and 11, confirming their DV nature. Franson interferometry verifies global frequency correlations with a visibility of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>97.6</b:mn> <b:mo>±</b:mo> <b:mn>0.6</b:mn> <b:mo>%</b:mo> </b:mrow> </b:math> and CV entanglement within individual frequency modes with a visibility exceeding <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>95</c:mn> <c:mo>%</c:mo> </c:mrow> </c:math> . Furthermore, based on the developed theoretical model, the generated HFEQs exhibit a Schmidt number that exceeds the upper bound <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>D</d:mi> </d:math> of conventional frequency-entangled qudits, certifying additional entanglement inherent to the hybrid structure. Our findings provide deeper insight into the physical nature of frequency-entangled qudits generated by quantum interference and introduce a resource for HD time-frequency quantum information processing.