Asymptotical Locking Tomography of High-Dimensional Entanglement*

Abstract

High-dimensional (HD) entanglement provides a very promising way of transcending the limitations of the two-dimensional entanglement between qubits for increasing channel capacity in many quantum protocols. In the pursuit of capitalizing on the HD entangled states, one of the central issues is to unambiguously and comprehensively quantify and reconstruct them. The full quantum state tomography is a unique solution, but it is undesirable and even impractical because the measurements increase rapidly in d 4 for a bipartite d-dimensional quantum state. Here we present a very efficient and practical tomography method—asymptotical locking tomography (ALT), which can harvest full information of bipartite d-dimensional entangled states by very few measurements less than 2d 2 only. To showcase the validity and reasonableness of our ALT, we carry out the test with the two-photon spin-orbital angular momentum hyperentangled states in a four-dimensional subspace. Besides high-efficiency and practicality, our ALT is also universal and can be generalized into multipartite HD entanglement and other quantum systems.

Fast Quantifier of High‐Dimensional Frequency Entanglement through Hong–Ou–Mandel Interference

“…[17,18] It is crucial to have a quantifier of the dimensionality of entanglement as measured in an experiment. [19][20][21][22] While the characterization of entanglement can typically be implemented by using quantum state tomography, [23,24] a concise yet efficient method for quantifying the dimensionality of frequency entanglement is still a formidable challenge, owing to both the difficulty of performing required superposition measurements in the frequency domain, [25] as well as the general challenges associated with performing full quantum state tomography in a large state space. In classical information theory, the number of independent communication channels of a signal is known as the Shannon number in the spirit of Shannon.…”

Characterization of Orbital Angular Momentum Quantum States Empowered by Metasurfaces

“…The certification and quantification of entanglement is a crucial task because maximally entangled pure states will become nonmaximally entangled or partially mixed states due to the dissipation and decoherence. The full state tomography is a feasible solution for this task, but the experimental measurement is too complex. The two-photon OAM pure states, separable or entangled, can be Schmidt decomposed into | Ψ ⟩ = prefix∑ m = − ∞ ∞ λ m false| m false⟩ ⊗ false|− m false⟩ where the coefficient λ m ( λ m 1 , m 2 , m 1 = m , m 2 = − m ) is the probability amplitude (satisfying the normalization condition, Σ|λ m 1 , m 2 | 2 = 1) of finding the signal photon with the OAM of m 1 ℏ and the idler photon with the OAM of m 2 ℏ in coincidence.…”

Optimization of Light Field for Generation of Vortex Knot

“…[4] For example, the most typical example is the orbital angular momentum (OAM), which has been widely studied. [5][6][7][8][9][10][11][12][13][14][15][16][17][18] (2) For the second one, the vortex line is closed in the three-dimensional light field, forming a complex knotted or linked topological structure. In mathematical language, the theory of knots and links studies the embedding mode of one or several closed curves in three-dimensional Euclidean space.…”