An increase in the dimension of state space for quantum key distribution (QKD) can decrease its fidelity requirements while also increasing its bandwidth. A significant obstacle for QKD with qu $d$ its ( $d\geq 3$ ) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both amplitude and phase. We propose such a sorter based on a multiplexed thick hologram, constructed e.g. from photo-thermal refractive (PTR) glass. We validate this approach using coupled-mode theory with parameters consistent with PTR glass to simulate a holographic sorter. The model assumes a three-dimensional state space spanned by three tilted planewaves. The utility of such a sorter for broader quantum information processing applications can be substantial.An increase in the dimension of state space for quantum key distribution (QKD) can decrease its fidelity requirements while also increasing its bandwidth. A significant obstacle for QKD with qu$d$its ($d\geq 3$) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both amplitude and phase. We propose such a sorter based on a multiplexed thick hologram, constructed e.g. from photo-thermal refractive (PTR) glass. We validate this approach using coupled-mode theory with parameters consistent with PTR glass to simulate a holographic sorter. The model assumes a three-dimensional state space spanned by three tilted planewaves. The utility of such a sorter for broader quantum information processing applications can be substantial.

Quantum Information and ComputationMar 1, 20113 citations

Projective quantum measurements on spatial modes of the photon with transmission volume holograms

Mark T. Gruneisen, James P. Black, Raymond C. Dymale +1 more

Transmission volume holograms are evaluated as quantum projectors operating on spatial modes of the photon in mutually unbiased bases (MUBs). With applications to free-space quantum key distribution (QKD) in mind, state spaces based on rectilinear and azimuthal phase modes (i.e. photon linear and orbital angular momenta) are considered. Rectilinear phase modulation is shown to result in both greater mode densities for a receiving aperture in the far field and better efficiency and cross-talk characteristics when volume holograms are used as de-multiplexing elements. Twoand four-dimensional state spaces are defined via rectilinear phase modes and the complex optical fields of the MUBs are calculated and generated with a spatial light modulator in order to record and subsequently illuminate transmission volume holograms. Using holograms prepared in lithium niobate, diffraction efficiencies are measured for the 36 permutations associated with projecting the six MUB states of a two-dimensional state space onto the same six MUB states. Quantum measurements associated with cascaded projection operations in a four-dimensional state space are performed using photo-thermo-refractive glass holograms. Experimental results show approximate agreement with the inner-product relationships that describe quantum projection probabilities.Transmission volume holograms are evaluated as quantum projectors operating on spatial modes of the photon in mutually unbiased bases (MUBs). With applications to free-space quantum key distribution (QKD) in mind, state spaces based on rectilinear and azimuthal phase modes (i.e. photon linear and orbital angular momenta) are considered. Rectilinear phase modulation is shown to result in both greater mode densities for a receiving aperture in the far field and better efficiency and cross-talk characteristics when volume holograms are used as de-multiplexing elements. Twoand four-dimensional state spaces are defined via rectilinear phase modes and the complex optical fields of the MUBs are calculated and generated with a spatial light modulator in order to record and subsequently illuminate transmission volume holograms. Using holograms prepared in lithium niobate, diffraction efficiencies are measured for the 36 permutations associated with projecting the six MUB states of a two-dimensional state space onto the same six MUB states. Quantum measurements associated with cascaded projection operations in a four-dimensional state space are performed using photo-thermo-refractive glass holograms. Experimental results show approximate agreement with the inner-product relationships that describe quantum projection probabilities.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIENov 19, 20121 citation

Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate

Laura Serino, Christof Eigner, Benjamin Brecht +1 more

We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to 0.958 ± 0.030 at the single-photon level.We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to 0.958 ± 0.030 at the single-photon level.

arXiv:2410.03606Optics ExpressDec 19, 20247 citations

High-dimensional quantum key distribution using a multi-plane light converter

Ohad Lib, Kfir Sulimany, Mateus Araújo +2 more

High-dimensional quantum key distribution (QKD) offers higher information capacity and stronger resilience to noise compared with its binary counterpart. However, these advantages are often hindered by the difficulty of realizing the required high-dimensional measurements and transformations. Here, we implement a large-scale multi-plane light converter (MPLC) and program it as a high-dimensional mode sorter of spatial modes for QKD. Using the MPLC, we demonstrate five-dimensional QKD with six mutually unbiased bases and 25-dimensional QKD with two mutually unbiased bases in the same experimental setup. Furthermore, we propose a construction of pairs of mutually unbiased bases that are robust to experimental errors, with measurement complexity scaling only with the square root of the encoded dimension. This approach paves the way for QKD implementations in higher dimensions.High-dimensional quantum key distribution (QKD) offers higher information capacity and stronger resilience to noise compared with its binary counterpart. However, these advantages are often hindered by the difficulty of realizing the required high-dimensional measurements and transformations. Here, we implement a large-scale multi-plane light converter (MPLC) and program it as a high-dimensional mode sorter of spatial modes for QKD. Using the MPLC, we demonstrate five-dimensional QKD with six mutually unbiased bases and 25-dimensional QKD with two mutually unbiased bases in the same experimental setup. Furthermore, we propose a construction of pairs of mutually unbiased bases that are robust to experimental errors, with measurement complexity scaling only with the square root of the encoded dimension. This approach paves the way for QKD implementations in higher dimensions.

arXiv:2403.04210Optica QuantumFeb 24, 202524 citations

Higher dimensional quantum communication in a curved spacetime: an efficient simulation of the propagation of the wavefront a photon

Warner A. Miller, Paul M. Alsing, Doyeol Ahn

A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channels tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channels tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.

arXiv:1812.09644SPIE Quantum Information Science, Sensing, and ComputationMay 16, 20181 citation

Holographic generation of complex fields with spatial light modulators: application to quantum key distribution

Mark T. Gruneisen, Warner A. Miller, Raymond C. Dymale +1 more

There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.

arXiv:0805.4392Applied OpticsOct 10, 200779 citations

An increase in the dimension of state space for quantum key distribution (QKD) can decrease its fidelity requirements while also increasing its bandwidth. A significant obstacle for QKD with qu

d

its (

d\geq 3

) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both amplitude and phase. We propose such a sorter based on a multiplexed thick hologram, constructed e.g. from photo-thermal refractive (PTR) glass. We validate this approach using coupled-mode theory with parameters consistent with PTR glass to simulate a holographic sorter. The model assumes a three-dimensional state space spanned by three tilted planewaves. The utility of such a sorter for broader quantum information processing applications can be substantial.