General scheme for complete high-dimensional Bell state measurement

Zhi Zeng; Zhi Zeng

doi:10.1364/OL.476425

Optics Letters
Vol. 47,
Issue 22,
pp. 5817-5820
(2022)
•https://doi.org/10.1364/OL.476425

General scheme for complete high-dimensional Bell state measurement

Zhi Zeng

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Zhi Zeng, "General scheme for complete high-dimensional Bell state measurement," Opt. Lett. 47, 5817-5820 (2022)

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Related Topics
Table of Contents Category
- Quantum Optics and Quantum Communication
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: September 22, 2022
- Manuscript Accepted: October 16, 2022
- Published: November 3, 2022

Abstract

We theoretically propose a simple and efficient scheme for the complete analysis of high-dimensional Bell states in N dimensions. The mutually orthogonal high-dimensional entangled states can be unambiguously distinguished by obtaining the parity and relative phase information of entanglement independently. Based on this approach, we present the physical realization of photonic four-dimensional Bell state measurement with the current technology. The proposed scheme will be useful for quantum information processing tasks that utilize high-dimensional entanglement.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the author upon reasonable request.

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Initial State	Possible Detections in Auxiliary Mode
$\| ψ_{n 0}^{P} ⟩$	$a a$ , $b b$ , $c c$ , $d d$
$\| ψ_{n 1}^{P} ⟩$	$a b$ , $b c$ , $c d$ , $d a$
$\| ψ_{n 2}^{P} ⟩$	$a c$ , $b d$ , $c a$ , $d b$
$\| ψ_{n 3}^{P} ⟩$	$a d$ , $b a$ , $c b$ , $d c$

Initial State	Possible Detections in Path Mode
$\| ψ_{0 m}^{P} ⟩$	$00$ , $13$ , $22$ , $31$
$\| ψ_{1 m}^{P} ⟩$	$03$ , $12$ , $21$ , $30$
$\| ψ_{2 m}^{P} ⟩$	$02$ , $11$ , $20$ , $33$
$\| ψ_{3 m}^{P} ⟩$	$01$ , $10$ , $23$ , $32$

Initial State	Possible Detections in Auxiliary Mode
$\| ψ_{n 0}^{P} ⟩$	$a a$ , $b b$ , $c c$ , $d d$
$\| ψ_{n 1}^{P} ⟩$	$a b$ , $b c$ , $c d$ , $d a$
$\| ψ_{n 2}^{P} ⟩$	$a c$ , $b d$ , $c a$ , $d b$
$\| ψ_{n 3}^{P} ⟩$	$a d$ , $b a$ , $c b$ , $d c$

Initial State	Possible Detections in Path Mode
$\| ψ_{0 m}^{P} ⟩$	$00$ , $13$ , $22$ , $31$
$\| ψ_{1 m}^{P} ⟩$	$03$ , $12$ , $21$ , $30$
$\| ψ_{2 m}^{P} ⟩$	$02$ , $11$ , $20$ , $33$
$\| ψ_{3 m}^{P} ⟩$	$01$ , $10$ , $23$ , $32$

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Equations (12)

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