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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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¹H NMR Signal Multiplicity: Splitting Patterns01:13

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
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The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
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¹H NMR: Complex Splitting01:13

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A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
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Realizing multi-user continuous-variable quantum key distribution via a shared entangled source and passive beam

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    This study introduces a continuous-variable quantum passive optical network (CV-QPON) using a shared entangled source. The new protocol significantly enhances secret key rates and network scalability for quantum internet development.

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    Area of Science:

    • Quantum Communication
    • Quantum Networking
    • Information Security

    Background:

    • Developing a high-rate, cost-effective, and secure quantum communication network is essential for the quantum internet.
    • Placing a shared entangled source at a central node enables efficient quantum resource utilization in a star-shaped network.

    Purpose of the Study:

    • To propose a continuous-variable quantum passive optical network (CV-QPON) utilizing a shared entangled source.
    • To evaluate the security and performance of the CV-QPON under different source characterization scenarios.

    Main Methods:

    • Implementation of a continuous-variable quantum passive optical network (CV-QPON) with a shared entangled source.
    • Security evaluation using both fully and partially characterized mixed entangled states.
    • Application of a biased basis scheme to enhance protocol performance.

    Main Results:

    • The renovated protocol outperforms previous methods in secret key rate, transmission distance, user capacity, and noise tolerance.
    • A 7 dB squeezing entangled source can support 256 users over 50 km with a fully characterized source.
    • With a partially characterized source, a 7 dB squeezing source supports 64 users over 30 km, and 128 users over 10 km.

    Conclusions:

    • The proposed CV-QPON scheme offers a practical pathway for low-cost, high-rate, secure, and large-scale quantum networks.
    • Relaxing security assumptions for the central node in partially characterized scenarios is crucial for downstream CV-QPON systems.
    • Advancements in integrated entangled sources make this scheme a promising approach for future quantum communication networks.