Multi-photon entanglement in high dimensions (1509.02561v1)

Abstract: Entanglement lies at the heart of quantum mechanics $-$ as a fundamental tool for testing its deep rift with classical physics, while also providing a key resource for quantum technologies such as quantum computation and cryptography. In 1987 Greenberger, Horne, and Zeilinger realized that the entanglement of more than two particles implies a non-statistical conflict between local realism and quantum mechanics. The resulting predictions were experimentally confirmed by entangling three photons in their polarization. Experimental efforts since have singularly focused on increasing the number of particles entangled, while remaining in a two-dimensional space for each particle. Here we show the experimental generation of the first multi-photon entangled state where both $-$ the number of particles and the number of dimensions $-$ are greater than two. Interestingly, our state exhibits an asymmetric entanglement structure that is only possible when one considers multi-particle entangled states in high dimensions. Two photons in our state reside in a three-dimensional space, while the third lives in two dimensions. Our method relies on combining two pairs of photons, high-dimensionally entangled in their orbital angular momentum, in such a way that information about their origin is erased. Additionally, we show how this state enables a new type of "layered" quantum cryptographic protocol where two parties share an additional layer of secure information over that already shared by all three parties. In addition to their application in novel quantum communication protocols, such asymmetric entangled states serve as a manifestation of the complex dance of correlations that can exist within quantum mechanics.

• The paper demonstrates the first experimental generation of a multi-photon entangled state in (3,3,2) dimensions using orbital angular momentum.
• It introduces an innovative OAM beam-splitter setup with dove prisms to achieve asymmetric entanglement.
• It achieves a fidelity of 0.801±0.018, confirming genuine multipartite high-dimensional quantum entanglement.

Multi-Photon Entanglement in High Dimensions: A Review

The paper "Multi-photon entanglement in high dimensions" presents a significant contribution to the paper of quantum entanglement by advancing both the number of particles and dimensions in entanglement experiments. This work marks the first experimental generation of a multi-photon entangled state where both metrics exceed two, showcasing an asymmetric entanglement structure. The researchers achieve this by entangling two photons in a three-dimensional space and another photon in a two-dimensional space, thus creating an entangled state in $(3,3,2)$ dimensions. The methodological framework of their experiment centers on the orbital angular momentum (OAM) of photons, taking advantage of its discrete and unbounded state space.

Experiment and Methodology

The experimental setup involves the coherent combination of two pairs of high-dimensionally entangled photons, resulting in the erasure of information about their origins. This method parallels previous work which utilized polarizing beam-splitters to entangle photons in polarization states. To accommodate the spatial freedom offered by OAM, the authors introduce an OAM beam-splitter, implemented through a Mach-Zehnder interferometer equipped with dove prisms. This apparatus discriminates between odd and even OAM values to produce entangled states with specified parity.

Results and Observations

The researchers manage to create a unique three-photon entangled state with asymmetric dimensionality indices of $(3,3,2)$. Noteworthy is the entanglement's asymmetric structure, which challenges traditional symmetric configurations widely documented in previous entanglement studies. To verify genuine multi-partite entanglement, the paper calculates a fidelity of $F_{\text{exp}}=0.801\pm0.018$, transcending the maximum achievable fidelity for lower-dimensional configurations by seven standard deviations. Such results confirm that their generated state is genuinely multipartite entangled in high dimensions, specifically in orbital angular momentum.

Implications and Future Directions

The theoretical and practical implications of this paper are expansive. The creation of high-dimensional entangled states suggests further exploration into the field of layered quantum cryptographic protocols, permitting asymmetric information sharing among multiple parties. As depicted, when Alice, Bob, and Carol share an asymmetric $(3,3,2)$ entangled state, they can encrypt quantum-secured messages with an additional layer of confidentiality shared only between Alice and Bob using the same quantum state.

Looking forward, the methodology applied in this work can be enhanced to form more nuanced and complex quantum states, pushing the boundaries of quantum networks. The potential to develop even more versatile states lays the groundwork for future advancements in quantum communication and computing.

Conclusion

This paper elucidates a new paradigm in studying multipartite quantum entanglement by stepping beyond the conventional two-photon, two-dimensional entanglement regimes. The manifestation of asymmetric entanglement within multi-photon and multi-dimensional frameworks introduces a new dimension to apply quantum entanglement in practical applications like secure layered communication, with implications for future quantum technologies. The roads paved by this research beckon future exploration into broader experimental studies of entangled states, facilitating a progressive understanding of quantum entanglement's applications in sophisticated quantum networks.