Hyperentanglement in intermediate phase-space planes: benchmarking a photon-pair source for quantum key distribution
Murilo H. Magiotto, Millena B. Novaes, Wesley B. Cardoso, Ardiley T. Avelar, 1 Paulo H. Souto Ribeiro, Stephen P. Walborn, Guilherme L. Zanin, Rafael M. Gomes
quant-phSubmitted Oct 14, 2026• Announced Oct 15, 2026• 0 citations
We characterize a source of photon pairs simultaneously entangled in polarization and in the transverse spatial degree of freedom, with the spatial measurements performed in intermediate planes of the fractional Fourier transform. The source consists of two crossed type-I crystals in a non-collinear geometry, such that the transverse variables carry information about the crystal of origin. Detection in the crystal plane reveals this information completely and destroys the polarization entanglement, so that a scheme using the near and far fields as conjugate spatial bases cannot support a parallel polarization channel. In intermediate planes both spatial bases combine position and momentum, such that the which-crystal information is partially erased, and the polarization entanglement survives in all four combinations of spatial bases. Applying Bell and Einstein-Podolsky-Rosen criteria to the same photon pairs certifies both degrees of freedom simultaneously. We evaluate quantum bit error rates and asymptotic secret key rates in each degree of freedom, and find that the source delivers two simultaneously usable channels per photon pair.
We characterize a source of photon pairs simultaneously entangled in polarization and in the transverse spatial degree of freedom, with the spatial measurements performed in intermediate planes of the fractional Fourier transform. The source consists of two crossed type-I crystals in a non-collinear geometry, such that the transverse variables carry information about the crystal of origin. Detection in the crystal plane reveals this information completely and destroys the polarization entanglement, so that a scheme using the near and far fields as conjugate spatial bases cannot support a parallel polarization channel. In intermediate planes both spatial bases combine position and momentum, such that the which-crystal information is partially erased, and the polarization entanglement survives in all four combinations of spatial bases. Applying Bell and Einstein-Podolsky-Rosen criteria to the same photon pairs certifies both degrees of freedom simultaneously. We evaluate quantum bit error rates and asymptotic secret key rates in each degree of freedom, and find that the source delivers two simultaneously usable channels per photon pair.
Pairs of photons simultaneously entangled in their path and polarization degrees of freedom are used to measure the topological phase acquired by bipartite entangled states. Conditional phase local unitary operations having the polarization degree of freedom as the control variable are applied. Qudits of arbitrary dimensions are encoded on the photons transverse positions while polarization entanglement is used as an auxiliary resource for quantum interference measurements. With this scheme the fractional phases predicted for dimensions d = 2, 3 and 4 could be measured with visibilities for the interference curves beyond the limit allowed for classical sources, which is expected for a source of quantum correlated photons. The strategy of perform a quantum interferometry experiment with photons entangled in an auxiliary degree of freedom and apply unitary local operations conditioned to this auxiliary variable shows an increase to the signal to noise ratio, simplifies alignment and can be used in different applications. This offers an interesting perspective for the efficient implementation of phase gates in quantum computing with hyperentangled photon sources in polarization and path degrees of freedom. Furthermore, one can conjecture whether the measured phase can serve as a dimensionality identifier of the Hilbert space dimension for an unknown state preparation.
Hyperentanglement, the simultaneous and independent entanglement of quantum particles in multiple degrees of freedom, is a powerful resource that can be harnessed for efficient quantum information processing. In photonic systems, the two degrees of freedom (DOFs) often used to carry quantum and classical information are polarization and frequency, thanks to their robustness in transmission, both in free space and in optical fibers. Telecom-band hyperentangled photons generated in optical fibers are of particular interest because they are compatible with existing fiber-optic infrastructure and can be distributed over fiber networks with minimal loss. Here, we experimentally demonstrate the generation of telecom-band biphotons hyperentangled in both the polarization and frequency DOFs using a periodically poled silica fiber and observe entanglement concurrences above 0.95 for both polarization and frequency DOFs. Furthermore, by concatenating a Hong-Ou-Mandel interference test for frequency entanglement and full state tomography for polarization entanglement in a single experiment, we can demonstrate simultaneous entanglement in both the polarization and frequency DOFs. The states produced by our hyperentanglement source can enable protocols such as dense coding and high-dimensional quantum key distribution.
The successful employment of high-dimensional quantum correlations and its integration in telecommunication infrastructures is vital in cutting-edge quantum technologies for increasing robustness and key generation rate. Position-momentum Einstein-Podolsky-Rosen (EPR) entanglement of photon pairs are a promising resource of such high-dimensional quantum correlations. Here, we experimentally certify EPR correlations of photon pairs generated by spontaneous parametric down-conversion (SPDC) in a nonlinear crystal with type-0 phase-matching at telecom wavelength for the first time. To experimentally observe EPR entanglement, we perform scanning measurements in the near- and far-field planes of the signal and idler modes. We certify EPR correlations with high statistical significance of up to 45 standard deviations. Furthermore, we determine the entanglement of formation of our source to be greater than one, which gives evidence for the the high-dimensional entanglement between the photons. Operating at telecom wavelengths around 1550 nm, our source is compatible with today's deployed telecommunication infrastructure, thus paving the way for integrating sources of high-dimensional entanglement into quantum-communication infrastructures.
Abstract The successful employment of high-dimensional quantum correlations and its integration in telecommunication infrastructures is vital in cutting-edge quantum technologies for increasing robustness and key generation rate. Position-momentum Einstein-Podolsky-Rosen (EPR) entanglement of photon pairs are a promising resource of such high-dimensional quantum correlations. Here, we experimentally certify EPR correlations of photon pairs generated by spontaneous parametric down-conversion (SPDC) in a nonlinear crystal with type-0 phase-matching at telecommunication wavelength for the first time. To experimentally observe EPR entanglement, we perform scanning measurements in the near- and far-field planes of the signal and idler modes. We certify EPR correlations with high statistical significance of up to 45 standard deviations. Furthermore, we determine the entanglement of formation of our source to be greater than one, indicating a dimensionality of greater than 2. Operating at telecommunication wavelengths around 1550 nm, our source is compatible with today’s deployed telecommunication infrastructure, thus paving the way for integrating sources of high-dimensional entanglement into quantum-communication infrastructures.
Here, we present a proof-of-principle high-dimensional quantum key distribution (QKD) protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually unbiased bases, linked via a Fourier transform. One photon of the entangled pair is measured by the sender in a randomly chosen basis-either position or momentum-selected passively via a beam splitter. This projective measurement remotely prepares the partner photon in a corresponding spatial mode, which is sent to the receiver, who similarly performs a random measurement in one of the two bases. In this implementation, we achieve a photon information efficiency of 5.07 bits per photon using 90 spatial modes, and a maximum bit rate of 0.9 Kb/s with 361 modes. To assess the scalability of this spatial-mode encoding scheme, we theoretically show that using a brighter entangled photon source along with next-generation single-photon cameras - featuring improved quantum efficiency, timing and spatial resolution - this approach could achieve 9 bits per photon at 2000 spatial modes, and a bit rate of over 700 Mb/s at 4400 modes while accounting for finite-key effects. These results quantify the opportunities and performance bounds of spatially encoded, entanglement-based QKD and provide a benchmark for future high-dimensional quantum communication systems.
The distribution of quantum entanglement between distant parties is a key challenge in the pursuit of a worldwide quantum network. Quantum repeaters and optical satellite links have both been proposed to overcome the distance limitations of fiber-based quantum networks. In order to test the viability of a world spanning quantum satellite network, several proof-of-concept studies have already demonstrated high-fidelity transmission of photonic entanglement via terrestrial long-distance free-space links. With the recent launch of the Micius quantum satellite by the Chinese Academy of Sciences, the technological challenge of implementing this scheme in situ was overcome. All of these free-space experiments utilized entanglement in a two-dimensional state space, which in most cases was encoded in the polarization of photons. However, high-dimensional entanglement can yield significant benefits in quantum key distribution by increasing the secure key rate and enhancing the resilience to eavesdropping attacks. Energy-time entanglement is an established photonic degree of freedom (DOF); it is routinely used for the distribution of entanglement in fiber-based quantum cryptography networks but has only recently been considered as a viable option for atmospheric free-space quantum communications. The dimensionality can be further increased by exploiting simultaneous entanglement in several DOF. This so-called hyperentanglement has previously been used in various quantum protocols, but not yet been demonstrated outside a protected laboratory environment. For our proof-of-concept experiment (doi:10.1038/ncomms15971), we use energy-time and polarization hyperentanglement to distribute, for the first time, 4-dimensional entanglement via a 1.2-km-long intra-city free-space link. A source of hyperentangled photons and a detection module (Alice) were located in our lab and a receiver station (Bob) was located at a different university building. The source produced polarization entangled photon pairs via type-0 down-conversion in a Sagnac loop configuration. The emission time of a photon pair is uncertain within the significantly longer coherence time of the pump laser, thus resulting in an energy-time and polarization hyperentangled state. One photon was guided to a local measurement module and the partner photon was guided to a transmitter telescope on the roof of the institute. After transmission over the 1.2-km-long free-space link, the photons were received by a telescope and detected in Bob’s measurement module. The measurement modules for Alice and Bob each featured a polarization and an energy-time analyzer. We observe high-visibility two-photon interference in both polarization and energy-time subspaces. The measured visibilities certify entanglement in both subspaces individually. Additionally, they establish a lower bound on the Bell-state fidelity of the hyperentangled state of 0.94, thus certifying genuine 4-dimensional entanglement and 1.47 ebits of entanglement of formation. We have thus successfully distributed hyperentangled photon pairs via an intra-city free-space link under conditions of strong atmospheric turbulence. The transmission of quantum information embedded in a genuine high-dimensional state space under real-world link conditions is a first important step towards real-world implementations of advanced quantum information processing protocols in the future. In particular, it enables the implementation of high-dimensional QKD protocols over long-distance free-space links, and, ultimately, over satellite links with only minor changes to existing mission proposals.