Qubit-Qudit Entanglement Transfer Achieves High-Spin Nuclear Memory with Arbitrary Dimension

Scientists are exploring novel methods to enhance quantum communication and memory, and a new study details a promising approach utilising the unique properties of defect centres in materials. W. -R. Hannes, Guido Burkard, both from the Department of Physics and IQST at the University of Konstanz, demonstrate a scheme for transferring entanglement from qubits to qudits , quantum systems with higher dimensionality , using the nuclear spins within these defects. This research is significant because it offers a pathway to build more robust and efficient quantum networks, potentially enabling deterministic entanglement generation without continuous manipulation of the nuclear spins, and is applicable to systems like the germanium vacancy in diamond.

This breakthrough establishes a pathway towards scalable quantum networking, particularly benefiting systems with high-spin nuclei which offer larger Hilbert spaces and improved coherence times. Experiments show that this interaction facilitates the repeated transfer of entanglement from communication qubits, based on electron spins, to the memory qudits residing in the nuclear spins. This work opens exciting possibilities for advanced quantum information processing strategies, such as quantum error correction and measurement-based quantum computing.

The study establishes that high-spin nuclei offer a hardware-efficient structure for encoding fault-tolerant logical qubits, surpassing the limitations of traditional spin qubits. A single network node and a two-node quantum network with remote entanglement storage have already been realised using silicon-vacancy centres, and this new scheme extends these capabilities to higher-dimensional nuclear-spin platforms like the 73Ge germanium vacancy in diamond, which boasts a nuclear spin of I = 9/2. The researchers constructed iterative schemes for entanglement accumulation, revealing that a driving-free protocol can deterministically generate maximal entanglement when d is a power of two. For other qudit dimensions, the study proposes alternative schemes with enhanced transfer success rates or the generation of partially entangled states, offering flexibility for various applications.,.

Qudit Entanglement via Hyperfine Interaction and Spin Transfer

This work demonstrates that the naturally occurring Ising component of hyperfine interaction is crucial for this process, enabling the creation of entanglement across multiple qudits. Researchers. Data shows that for other values of ‘d’, the success rate is 1/d, but alternative schemes can be constructed to enhance transfer rates. Measurements confirm that even when perfect entanglement isn’t attainable, partially entangled states can still prove useful for certain quantum computing protocols. Researchers recorded that in a bipartite scenario, the focus is on generating any maximally entangled state, with the explicit form detailed only in specific cases.

Tests prove the viability of the vanadium 51V defect in silicon carbide with I = 7/2, attracting increasing attention as a promising platform. Furthermore, the work explores implanted group-V donors in silicon, including 75As with I = 3/2, 123Sb with I = 7/2, and 209Bi with I = 9/2, as potential candidates. Single rare-earth ions, coupled to aluminium nuclear spins with I = 5/2 or host spins like 141Pr with I = 5/2, 143Nd with I = 7/2, and 167Er with I = 7/2, are also considered. The researchers demonstrated that applying the driving-free scheme to qudits with spin numbers of 3/2 and 7/2 is possible, and for others, ‘d’ can be lowered to the next favorable number by leaving certain energy levels unoccupied during initialization.

The study introduces a method to assess two-qudit entanglement using the Schmidt decomposition, where singular values, or Schmidt coefficients, are calculated to quantify the entanglement. Results demonstrate that the von Neumann entropy of the reduced density matrix provides a unique entanglement measure for pure states, enabling precise characterization of the generated entangled states. This advancement promises to unlock new possibilities in quantum communication and computation.,.

Nuclear spins enable deterministic multipartite entanglement

The study confirms the generation of genuine multipartite entanglement through successive application of the scheme to neighbouring network nodes, with entanglement scaling more rapidly with the number of parties as the qudit dimension increases. This protocol holds particular promise for measurement-based quantum computation (MBQC), although preparing higher-dimensional cluster states for this application requires further investigation. The authors acknowledge a limitation in the need to satisfy specific conditions, detailed in the appendix, to ensure deterministic generation of maximal entanglement, specifically, certain matrix relationships must hold for all combinations of qubit parameters. Future work will likely focus on exploring the application of this scheme to larger quantum networks and investigating the preparation of dedicated states for MBQC, potentially unlocking higher-dimensional qudit versions of various quantum computation protocols.