Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Information and Measurement (QIM)

Two-Rebit Entanglement: Theory and Experiment

Jan Sperling, Nidhin Prasannan, Syamsundar De, Sonja Barkhofen, Benjamin Brecht, Christine Silberhorn

Published Jan 1, 2021• 2 citations
Publisher

Abstract

We characterize entanglement over real and complex, composite quantum systems. Methods are formulated and applied to simultaneously certify inseparability and separability for two rebits and two qubits, respectively.
DOI
10.1364/qim.2021.m2a.5

Related papers

Experimental entanglement characterization of two-rebit states

Nidhin Prasannan, Syamsundar De, Sonja Barkhofen +3 more

We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply rooted, yet rarely discussed question of why quantum states are described via complex numbers. With our experiment, we then realize two-photon polarization states that are entangled with respect to the notion of two rebits, comprising two two-level systems over real numbers. At the same time, the generated states are separable with respect to two complex qubits. Among other results, we reconstruct the best approximation of the generated states in terms of a real-valued, local expansion and show that this yields an incomplete description of our data. Conversely, the generated states are shown to be fully decomposable in terms of tensor-product states with complex wave functions. Thereby, we probe paradigms of quantum physics with modern theoretical tools and experimental platforms that are relevant for applications in quantum information science and technology and connected to the fundamentals of the quantum description of nature.

arXiv:2102.01450•Physical Review A•Apr 19, 2021•12 citations

Understanding quantum entanglement: Qubits, rebits and the quaternionic approach

Josep Amengual i Batle, Angel Ricardo Plastino, M. Casas +1 more

It has been recently pointed out by Caves, Fuchs, and Rungta [1] that real quantum mechanics (that is, quantum mechanics defined over real vector spaces [2–5]) provides an interesting foil theory whose study may shed some light on just which particular aspects of quantum entanglement are unique to standard quantum theory and which are more generic over other physical theories endowed with this phenomenon. Following this work, some entanglement properties of two-rebit systems are discussed and a comparison with the basic properties of two-qubit systems, i.e., the systems described by standard complex quantum mechanics, is made. The use of quaternionic quantum mechanics as applied to the phenomenon of entanglement is also discussed.

arXiv:quant-ph/0603060•Optics and Spectroscopy•May 1, 2003•17 citations

Proof of the inseparability of maximal entanglement

Matheus Pereira Lobo

We proof the inseparability of two maximally entangled qubits. Next we analyze four separability criteria for a general two-qubit system.

•Jul 20, 2019•8 citations

Uncertainty Inequality for the Entanglement of Both Two-rebits and Two-qubits States

Manuél Ávila

International Journal of Theoretical Physics•Jul 19, 2019•1 citation

The rebit three-tangle and its relation to two-qubit entanglement

William K. Wootters

The three-tangle is a measure of three-way entanglement in a system of three qubits. For a pure state, it can be understood as the residual entanglement not accounted for by pairwise entanglements between individual qubits. Here we define and evaluate the analogous quantity for three rebits (that is, binary systems in the real-amplitude variant of quantum theory). We find that the resulting formula is the same as in the complex case, except that an overall absolute value sign is missing. As a result, the rebit three-tangle can be negative, expressing the possibility of non-monogamous entanglement in real-amplitude quantum theory (for entanglement based on the convex-roof construction). We then relate the entanglement among three rebits to the entanglement of two qubits, by re-expressing the two-qubit state as a three-rebit state in the ubit model. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

arXiv:1402.2219•Journal of Physics A Mathematical and Theoretical•Oct 9, 2014•31 citations

Degree of entanglement for two qubits

Jing‐Ling Chen, Libin Fu, Abraham Albert Ungar +1 more

In this paper, we present a measure to quantify the degree of entanglement for two qubits in a pure state.

arXiv:quant-ph/0204162•Physical Review A•Apr 1, 2002•14 citations
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply rooted, yet rarely discussed question of why quantum states are described via complex numbers. With our experiment, we then realize two-photon polarization states that are entangled with respect to the notion of two rebits, comprising two two-level systems over real numbers. At the same time, the generated states are separable with respect to two complex qubits. Among other results, we reconstruct the best approximation of the generated states in terms of a real-valued, local expansion and show that this yields an incomplete description of our data. Conversely, the generated states are shown to be fully decomposable in terms of tensor-product states with complex wave functions. Thereby, we probe paradigms of quantum physics with modern theoretical tools and experimental platforms that are relevant for applications in quantum information science and technology and connected to the fundamentals of the quantum description of nature.
It has been recently pointed out by Caves, Fuchs, and Rungta [1] that real quantum mechanics (that is, quantum mechanics defined over real vector spaces [2–5]) provides an interesting foil theory whose study may shed some light on just which particular aspects of quantum entanglement are unique to standard quantum theory and which are more generic over other physical theories endowed with this phenomenon. Following this work, some entanglement properties of two-rebit systems are discussed and a comparison with the basic properties of two-qubit systems, i.e., the systems described by standard complex quantum mechanics, is made. The use of quaternionic quantum mechanics as applied to the phenomenon of entanglement is also discussed.
The three-tangle is a measure of three-way entanglement in a system of three qubits. For a pure state, it can be understood as the residual entanglement not accounted for by pairwise entanglements between individual qubits. Here we define and evaluate the analogous quantity for three rebits (that is, binary systems in the real-amplitude variant of quantum theory). We find that the resulting formula is the same as in the complex case, except that an overall absolute value sign is missing. As a result, the rebit three-tangle can be negative, expressing the possibility of non-monogamous entanglement in real-amplitude quantum theory (for entanglement based on the convex-roof construction). We then relate the entanglement among three rebits to the entanglement of two qubits, by re-expressing the two-qubit state as a three-rebit state in the ubit model. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.