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arXiv:2308.12327 · Physical Review C

Toward experimental determination of spin entanglement of nucleon pairs

Dong Bai

Published Mar 6, 2024• 22 citations
arXivHTMLPDF

Abstract

Nuclear entanglement is a flagship in the interdisciplinary direction of nuclear physics and quantum information science. Spin entanglement, a special kind of nuclear entanglement, is ubiquitous in nuclear structures and dynamics. Based on the idea of quantum state tomography, the problem of experimental determination of spin entanglement of two-nucleon pure states is studied directly within the scope of nuclear physics. It is shown that the amount of spin entanglement can be obtained by measuring three spin polarizations of one nucleon in polarization experiments. The errors from imperfect preparation of nucleon pairs are also analyzed. This work not only complements the existing literature of nuclear entanglement but also provides new opportunities for nuclear physics with polarized particles.

DOI
10.1103/physrevc.109.034001

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Nuclear entanglement is a flagship in the interdisciplinary direction of nuclear physics and quantum information science. Spin entanglement, a special kind of nuclear entanglement, is ubiquitous in nuclear structures and dynamics. Based on the idea of quantum state tomography, the problem of experimental determination of spin entanglement of two-nucleon pure states is studied directly within the scope of nuclear physics. It is shown that the amount of spin entanglement can be obtained by measuring three spin polarizations of one nucleon in polarization experiments. The errors from imperfect preparation of nucleon pairs are also analyzed. This work not only complements the existing literature of nuclear entanglement but also provides new opportunities for nuclear physics with polarized particles.
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Nucleon-nucleon scattering is a fundamental process in low-energy nuclear physics. Although its spin correlations have been studied intensively, few works take the perspective of quantum information science. In this work, I explore the quantum information aspects of spin correlations in the partially polarized neutron-proton scattering in the SSS wave. It is found that the spin mutual information, entanglement and discord of the out-states, when averaged over the possible in-states, all vary in a similar way with respect to the relative momentum. The novel connection between emergent symmetry and spin entanglement found by a previous study [Phys. Rev. Lett. 122, 102001 (2019)] could then be extended naturally to spin correlations beyond entanglement.
In this work, we have been working on the concept of quantum entanglement. At first, we studied the theory of entanglement in its characterization and measurement, introducing a new scheme for detection of entanglement. The new approach links molecular-spin entities involving nuclear spins to quantum computing as more appropriate physical systems of interest. Then, we continued with the realization of entanglement in experiments. NMR has been the first choice due to its well approved advantages for quantum computing. NMR, however, has not been an appropriate system for demonstrating entangled states. Through a mathematical proof, NMR with low spin polarization has been invalidated for true implementations of non-local quantum algorithms, particularly supserdense coding. The point is that high spin polarization is inevitably required to acquire entanglement while in the current NMR it has been a formidable task to get highly polarized nuclear spins. In order to acquire high spin polarization, introducing electron spins can be much effective because of its three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins. Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that enables us to deal with both electron and nuclear spins. Thus, in this context, it can be more appropriate device for quantum computing. We emphasize that (pseudo)entanglement and interconversion between the entangled states have been realized with ENDOR on extremely stable organic molecular-spin entities. The required experimental conditions to obtain true quantum entanglement are also discussed. The appropriate entanglement witness for the corresponding ensemble quantum computing is introduced and examined.
We describe a method in which the entanglement of any pure quantum state can be experimentally determined by a simple projective measurement, provided the state is available in a twofold copy. We propose implementations of this approach for various systems and discuss in detail its first experimental realization, which employed twin photons entangled in two degrees of freedom, prepared in identical polarization and momentum states. We analyze the effect of errors due to imperfect state preparation.
We established important relationships between entanglement measures and the order parameter (spin polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily manipulated by the NMR technique, experimentalists are presented with an opportunity to study the dynamic properties of entanglement, i.e., the creation and evolution of entangled states. Our approach may constitute the basis for researching the relations between the entanglement measures and measurable parameters of order in other quantum systems.
Quantum computation depends on quantum entanglement, a correlation between subsystems that cannot occur classically. A variety of theoretical measures exist for quantifying the degree entanglement in such schemes, all of which are functions of the system density matrix. How can the entanglement be measured experimentally? Using quantum tomography techniques developed for two photon entangled states, the density matrix can be reconstructed from the appropriate experimental data. In this case the state tomography gives the complete characterization of the physical system (for the relevant degree of freedom, such as spin or polarization). It gives information on both the degree of nonclassical correlation, that is entanglement, as well as the amount of decoherence in the system. In this proceedings we discuss the general state tomography procedure required to characterize a few qubit quantum computer, for any architecture.