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Science Advances

Manipulation of eight-dimensional Bell-like states

Ling‐Jun Kong, Rui Liu, Wen-Rong Qi, Zhou-Xiang Wang, Shuang‐Yin Huang, Qiang Wang, Chenghou Tu, Yongnan Li, Hui‐Tian Wang

Published Jun 1, 2019• 38 citations
Publisher

Abstract

High-dimensional Bell-like states are necessary for increasing the channel capacity of the quantum protocol. However, their preparation and measurement are still huge challenges, especially for the latter. Here, we prepare an initial eight-dimensional Bell-like state based on hyperentanglement of spin and orbital angular momentum (OAM) of the first and the third orders. We design simple unitary operations to produce eight Bell-like states, which can be distinguished completely in theory among each other. We propose and illustrate a multiple projective measurement scheme composed of only linear optical elements and experimentally demonstrate that all the eight hyperentangled Bell-like states can be completely distinguished by our scheme. Our idea of manipulating the eight Bell-like states is beneficial to achieve the 3-bit channel capacity of quantum protocol, opening the door for extending applications of OAM states in future quantum information technology.

DOI
10.1126/sciadv.aat9206

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High-dimensional Bell-like states are necessary for increasing the channel capacity of the quantum protocol. However, their preparation and measurement are still huge challenges, especially for the latter. Here, we prepare an initial eight-dimensional Bell-like state based on hyperentanglement of spin and orbital angular momentum (OAM) of the first and the third orders. We design simple unitary operations to produce eight Bell-like states, which can be distinguished completely in theory among each other. We propose and illustrate a multiple projective measurement scheme composed of only linear optical elements and experimentally demonstrate that all the eight hyperentangled Bell-like states can be completely distinguished by our scheme. Our idea of manipulating the eight Bell-like states is beneficial to achieve the 3-bit channel capacity of quantum protocol, opening the door for extending applications of OAM states in future quantum information technology.
Quantum protocols require access to large-scale entangled quantum states, due to the requirement of channel capacity. As a promising candidate, the high-dimensional orbital angular momentum (OAM) entangled states have been implemented, but only one of four OAM Bell states in each individual subspace can be distinguished. Here we demonstrate the first realization of complete OAM Bell-state measurement (OAM-BSM) in an individual subspace, by seeking the suitable unitary matrix performable using only linear optics and breaking the degeneracy of four OAM Bell states in ancillary polarization dimension. We further realize the superdense coding via our complete OAMBSM with the average success probability of ~82% and the channel capacity of ~1.1(4) bits. This work opens the window for increasing the channel capacity and extending the applications of OAM quantum states in quantum information in future.
Orbital angular momentum (OAM) entanglement states have great potential in enhancing the information capacity in quantum communications. To make full use of the OAM degree of freedom, the measurement and distinction of OAM Bell states become a key step that needs to be accomplished. However, there is still no solution to achieve complete distinction of OAM Bell states at the single-photon level. Here we demonstrate the complete OAM Bell-state measurement without auxiliary photons by using linear optics. Furthermore, we propose a quantum communication network via OAM Bell-state multiplexing, perform a proof-of-principle experiment in the first- and second-order OAM subspaces for two users, and achieve average success probabilities of obtaining information of 91.6% for User-I and 89.1% for User-II. In principle, our scheme allows more users to be added by using high-order OAM Bell states. Our research extends the manipulation method for high-dimensional quantum states and paves the way for the application of OAM multiplexing in quantum communications.
The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.
Distinguishing limit of Bell states for any nnn-photon DDD-dimensional hyperentanglement
Bell state measurement is crucial to quantum information protocols, but it is impossible to unambiguously distinguish all the Bell states encoded in multi-photon using only linear optics. There is a maximum number of distinguished Bell states, i.e. distinguising limit which is very important for increasing the channel capacity of quantum communications. In this paper, we separate nnn-photon DDD-dimensional hyperentanglement into two groups. For the first group of UUU (G1G_1G1​), we obtain the limit N1=nD−(n−1){N_1} = nD - (n - 1)N1​=nD−(n−1), which can be applied for both bosons' and fermions' cases. We further discuss the limit NNN for any nDnDnD system with the second group of UUU (G2G_2G2​), inferring that at least Dn−1{D^{n - 1}}Dn−1 Bell states can be distinguished due to the symmetry of Bell states. Obviously, N1≤N2{N_1} \le {N_2}N1​≤N2​ for those systems with n>2n>2n>2. Finally, we theoretically design an optical setup for Bell state measurement of two-photon eight-dimensional hyperentanglement of spin, path and orbital angular momentum (OAM) and distinguish 15 classes of 64 Bell states. Our results provide a theoretical basis and practical reference to increase the channel capacity of the quantum communication.
Abstract Electromagnetic waves have both spin momentum and orbital angular momentum (OAM). Light carrying OAM has broad applications in micro-particle manipulation, high-precision optical metrology, and potential high-capacity optical communications. In the concept of quantum information, a photon encoded with information in its OAM degree of freedom enables quantum networks to carry much more information and increase their channel capacity greatly compared with those of current technology because of the inherent infinite dimensions for OAM. Quantum memories are indispensable to construct quantum networks. Storing OAM states has attracted considerable attention recently, and many important advances in this direction have been achieved during the past few years. Here we review recent experimental realizations of quantum memories using OAM states, including OAM qubits and qutrits at true single photon level, OAM states entangled in a two-dimensional or a high-dimensional space, hyperentanglement and hybrid entanglement consisting of OAM and other degree of freedom in a physical system. We believe that all achievements described here are very helpful to study quantum information encoded in a high-dimensional space.
We present a theoretical scheme for the complete Bell state measurement (BSM) for high-dimensional hyperentangled photons in polarization and path degrees of freedom (DOFs), in which the polarization entanglement is in two-dimensional Hilbert space and the path entanglement is in four-dimensional Hilbert space. This 2×4-dimensional photonic quantum system contains 64 mutually orthogonal high-dimensional hyperentangled Bell states, which can be unambiguously discriminated by using weak cross-Kerr nonlinearity, linear optical element, and single-photon detector. This is the first complete BSM scheme for high-dimensional hyperentangled photons in two DOFs assisted by the quantum nonlinear effect, and we also demonstrate its application in the quantum superdense coding protocol, which allows the transmission of log 2 64=6 bits of classical information via just sending one photon. Moreover, our scheme only requires the achievable small nonlinear phase shift, and it can provide new avenues for other BSM-based quantum information technologies involving photonic high-dimensional hyperentanglement.