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arXiv:2004.14956

Multi-Photon, Multi-Dimensional Hyper-Entanglement using Higher-Order Radix qudits with Applications to Quantum Computing, QKD and Quantum Teleportation

Solyman Ashrafi, Campbell, Logan

Published Apr 30, 2020• 0 citations
arXivHTMLPDF

Abstract

Google recently announced that they had achieved quantum supremacy with 53 qubits (base-2 binaries or radix-2), corresponding to a computational state-space of dimension 253 (about 1016). Google claimed to perform computations that took 200 seconds on their quantum processor that would have taken 10,000 years to accomplish on a classical supercomputer [1]. However, achieving superposition and entanglement of 53 qubits is not an easy task given the environmental noise that decoheres the qubits. In this paper, we claim that one can potentially achieve a similar computational dimension with fewer qudits (not qubits) where each qudit is of a higher radix (greater than 2) using a photonics system (i.e. 16 qudits with radix-10). This paper is a collaborative development between industry and NxGen Partners to explore such an approach. There is a Raytheon technology that uses a Free-Space Optical (FSO) Fabry-Perot Etalon that eliminates the need for adaptive optics [2, 3]. The NxGen technology uses multiple Orbital Angular Momentum (OAM) modes as a new degree of freedom for quantum computing and a multi-dimensional QKD [4-7]. We also claim that the convergence of both broadband, secure communications, quantum computing and quantum teleportation is only possible in a photonics realization. Therefore, the use of photonic qudits allows the extension of security and capacity of the quantum teleportation beyond what was achieved by Chinese Micius quantum satellite [8]. Both the defense and commercial computing industries need such quantum computing systems. A new measure is introduced with computational state-space dimension, high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains. This new measure which we call quantum capacity is a practical way to measure and compare progress toward improved system structure of a universal quantum computer.

DOI
10.48550/arxiv.2004.14956

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Google recently announced that they had achieved quantum supremacy with 53 qubits (base-2 binaries or radix-2), corresponding to a computational state-space of dimension 253 (about 1016). Google claimed to perform computations that took 200 seconds on their quantum processor that would have taken 10,000 years to accomplish on a classical supercomputer [1]. However, achieving superposition and entanglement of 53 qubits is not an easy task given the environmental noise that decoheres the qubits. In this paper, we claim that one can potentially achieve a similar computational dimension with fewer qudits (not qubits) where each qudit is of a higher radix (greater than 2) using a photonics system (i.e. 16 qudits with radix-10). This paper is a collaborative development between industry and NxGen Partners to explore such an approach. There is a Raytheon technology that uses a Free-Space Optical (FSO) Fabry-Perot Etalon that eliminates the need for adaptive optics [2, 3]. The NxGen technology uses multiple Orbital Angular Momentum (OAM) modes as a new degree of freedom for quantum computing and a multi-dimensional QKD [4-7]. We also claim that the convergence of both broadband, secure communications, quantum computing and quantum teleportation is only possible in a photonics realization. Therefore, the use of photonic qudits allows the extension of security and capacity of the quantum teleportation beyond what was achieved by Chinese Micius quantum satellite [8]. Both the defense and commercial computing industries need such quantum computing systems. A new measure is introduced with computational state-space dimension, high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains. This new measure which we call quantum capacity is a practical way to measure and compare progress toward improved system structure of a universal quantum computer.
Multiple photonic degrees of freedom can be explored to generate high-dimensional quantum states; commonly referred to as `qudits'. Qudits offer several advantages for quantum communications, including higher information capacity, noise resilience and data throughput, and lower information loss over different propagation mediums (free space, optical fibre, underwater) as compared to conventional qubits based communication system. However, qudits have been little exploited in literature, owing to their difficulty in transmission and detection. In this paper, for the first time, we develop and formulate the theoretical framework for transmission of classical information through entanglement distribution of qudits over two quantum channels in superposition of alternative causal order. For the first time we i) engineer quantum switch operation for 2-qudit systems and ii) formulate theoretical system model for entanglement distribution of qudits via quantum switch. Results show that entanglement distribution of a qudit provides a considerable gain in fidelity even with increase in noise.
Quantum teleportation, lying at the heart of a variety of quantum technologies, has inspired a widespread of research activities, most of which focused on 2-dimensional qubit states. Multilevel systems, qudits, promise to upgrade and inspire new technical developments in high-dimensional Hilbert space. Whereas, for high-dimensional teleportation, it routinely necessitates several ancillary photons in linear optical schemes. A fundamental open challenge remains as to whether we can teleport qudit states with bipartite entanglement only. Here we demonstrate such a high-dimensional teleportation using photonic orbital angular momentum (OAM). The so-called "perfect vortices" are exploited both for conducting the prerequisite entanglement concentration to prepare high-dimensional yet maximal OAM entanglement, and for performing faithful high-dimensional Bell sate measurements (HDBSM) based on sum-frequency generation. We experimentally achieve the average teleportation fidelity 0.8788$\pm$0.048 for a complete set of 3-dimensional mutually unbiased bases, for instance, conditional on three specific HDBSM results. More importantly, we succeed in realizing the first quantum teleportation of optical images by exploring full transverse spatial entanglement. From the multi-pixel field of view in the teleported images recorded by the ICCD camera, we estimate the effective channel capacity up to \k{appa} > 100. Our scheme holds promise for future high-volume quantum image transmission.
Abstract Quantum teleportation lies at the heart of a variety of quantum technologies, most of which, however, focused on 2-dimensional qubit states only. A fundamental open challenge remains as to whether we can teleport multilevel qudit states with bipartite entanglement. Here, we demonstrate such a high-dimensional teleportation using photonic orbital angular momentum (OAM). We exploit “perfect vortices” for preparing high-dimensional yet maximal OAM entanglement and for performing faithful high-dimensional Bell sate measurements (HDBSM) based on sum-frequency generation. We experimentally achieve the average teleportation fidelity 0.8788±0.048 for a complete set of 3-dimensional mutually unbiased bases. More importantly, we succeed in realizing the first quantum teleportation of optical images, with the effective channel capacity κ > 100. Our scheme holds promise for future high-volume quantum image transmission.
Quantum information processing and communication techniques rely heavily upon entangled quantum states, and this dependence motivates the development of methods and systems to generate entanglement. Much research has been dedicated to state preparation for radix-2 qubits, and due to the pursuit of entangled states, the Bell state generator and its generalized forms where the number of entangled qubits is greater than two have been defined. In this work, we move beyond radix-2 and propose techniques for quantum state entanglement in high-dimensional systems through the generalization of the binary bipartite entanglement states. These higher-radix quantum informatic systems are composed of n quantum digits, or qudits, that are each mathematically characterized as elements of an r -dimensioned Hilbert vector space where r > 2. Consequently, the wave function is a time-dependent state vector of dimension r n . The generalization of the binary controlled-NOT to the controlled-modulo-addition gate, the concept of partial versus maximal entanglement, and architectures for generating higher-radix entangled states for the partial and maximal case are all presented.
Qudits, the d-dimensional extension of qubits, open new perspectives in several fields, from fundamental quantum mechanics to quantum cryptography. Although photon polarization is a privileged choice for qubits encoding, it is not suitable for the physical realization of qudits. However, in order to realize multidimensional quantum systems, other degrees of freedom of single photons such as path or orbital angular momentum are available. When two or more degrees of freedom are exploited simultaneously we refer to "hybrid encoding". It is possible for instance to encode information in a four dimensional (ququart) hybrid space spanned by polarization and a bidimensional orbital angular momentum subspace of a single photon. Here we present how high dimensional hybrid systems can be exploited to overcome a major limitation of quantum communication: the need of a shared reference frame. Indeed the joint action of polarization and orbital angular momentum of hybrid ququarts can be exploited to realize quantum communication without a shared reference frame. We experimentally showed that, by using a proper subspace of hybrid ququart space, it is possible to perform any quantum communication protocol and violate CHSH inequalities without any information about the reference frame orientation of the two parties (except the direction of propagation of the photons). Such feature could find application in satellite based communication schemes.
Photons can carry quantum information not only in two-level systems (qubits) but also in d-level systems known as qudits. A single photon distributed across d optical modes can encode up to log2(d) qubits of information, allowing for more efficient use of quantum resources and increased resilience to noise. This advantage, however, comes at a price: implementing quantum gates and performing measurements in high-dimensional Hilbert spaces is significantly more demanding than in the qubit case. To tackle these challenges, I will present our recent work developing new protocols and optical hardware that enable quantum communication and computation with high-dimensional qudits encoded in the temporal or spatial modes of single and entangled photons. I will discuss our experimental implementations of quantum key distribution using weak coherent pulses [Sulimany et al., NPJ Quantum Information 11, 16 (2025)], single photons from quantum dots [Halevi et al., Optica Quantum 2, 351 (2024)], and entangled photon pairs [Lib et al., Optica Quantum 3, 182 (2025)]. In the latter, we demonstrated projective measurements in two mutually unbiased bases for d=25d = 25d=25 using a multi-plane light converter (MPLC). I will also show how the same MPLC platform can be used to perform elementary operations in measurement-based quantum computation with high-dimensional cluster states [Lib and Bromberg, Nat. Photonics 18, 1218 (2024)]. Throughout the talk, I will discuss the tradeoffs between qubit- and qudit-based approaches and highlight the regimes where high-dimensional systems offer a practical advantage.