[[Quantum Noise]] [[Coherent State]] [[Non-orthogonal states]] [[Quantum measurements]] [[Holevo's Theorem]] Our latest research focuses on optimizing quantum key distribution (QKD) protocols by leveraging the unique properties of nonorthogonal states. - **Protocol Flexibility**: When a large fraction of the signal is intercepted, our protocol utilizes weak coherent states of light, similar to other established protocols. However, when the intercepted fraction is minimal, we can increase the light's intensity. This adjustment enhances the performance metrics of our protocol while only slightly reducing the "quantum-ness" of the light. - **Foundational Research**: Charles H. Bennett's paper, [“Quantum cryptography using any two nonorthogonal states”](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.68.3121) provides a foundational understanding. It explains that “bright coherent states, typically nearly orthogonal, become significantly nonorthogonal when attenuated.” This insight is crucial for our protocol's adaptability. - ### Bright [[Coherent State]]: - **Orthogonality**: Bright coherent states, which have large amplitudes, are typically nearly orthogonal. This means that they can be distinguished from one another with high accuracy because the overlap between their wave functions is minimal. - **Phase Space Representation**: In phase space, bright coherent states are represented as points with small [[uncertainty]] circles, indicating precise amplitude and phase information. - ### Effect of Attenuation: - **Attenuation**: When a bright coherent state is attenuated, its amplitude decreases. This process can be likened to reducing the intensity of a light beam. - **Nonorthogonality**: As the amplitude decreases, the coherent states become significantly nonorthogonal. This means that the overlap between their wave functions increases, making it harder to distinguish one state from another with certainty. - **Quantum Mechanical Implication**: The non-orthogonality arises due to the fundamental quantum mechanical principle that non-orthogonal states cannot be perfectly discriminated. This property is crucial in quantum communication and quantum key distribution, where the ability to distinguish between different states impacts the security and efficiency of the protocols [[1](https://www.st-andrews.ac.uk/~qoi/QuInf_research.html)][[6](https://en.wikipedia.org/wiki/Coherent_state)]. - ### Applications and Challenges: - **Quantum Key Distribution (QKD)**: In QKD protocols like differential-phase-shift quantum key distribution, non-orthogonal states are used to ensure security. The increased non-orthogonality due to attenuation can present challenges in these protocols [[4](https://www.researchgate.net/publication/235596157_Differential-phase-shift_quantum_key_distribution_using_coherent_light)]. - **Measurement and Detection**: Techniques like homodyne detection, which involve interfering a signal with a local oscillator, are used to measure and differentiate these states. However, the increased overlap due to attenuation complicates this process [[2](https://royalsocietypublishing.org/doi/10.1098/rsta.2016.0235)]. In summary, the attenuation of bright coherent states leads to a significant increase in their non-orthogonality, affecting their distinguishability and posing challenges in quantum communication and measurement applications. - **Orthogonality and Measurement**: Orthogonal states, like the qubit states |0⟩ and |1⟩, can be distinguished by specific measurements, such as the computational basis. [[Non-orthogonal states]], however, are harder to distinguish, which makes them invaluable in cryptography. The initial sentences of the second paragraph in these [Cambridge lecture notes](https://che01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.qi.damtp.cam.ac.uk%2Ffiles%2FQIC-3.pdf&data=05%7C01%7Ckaran%40terraquantum.swiss%7Cea042cdd2aaa402fb9a008dbcf4d1c0a%7Ca29b5ad8d9e147ba97162ea42f6f9bd0%7C0%7C0%7C638331702314708440%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=3IOH5532ceGn1oJCmVTxqN9bZlp95Xhj1XfTzBkmRcs%3D&reserved=0) elucidate the importance of these measurements. - **Literature and Validation**: Have you reviewed this [paper](https://che01.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fpdf%2Fquant-ph%2F0211131.pdf&data=05%7C01%7Ckaran%40terraquantum.swiss%7Cea042cdd2aaa402fb9a008dbcf4d1c0a%7Ca29b5ad8d9e147ba97162ea42f6f9bd0%7C0%7C0%7C638331702314708440%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=zVrfsuCAO1Blt0cWWelGB5gvL1h4VLZONwxfbQT%2Fels%3D&reserved=0)? It explores quantum features like non-orthogonality and quantum measurement, driving a new type of protocol akin to ours. This work is a cornerstone in the field, frequently cited and foundational for further research. - **Distinctive Features**: Our protocol stands out by utilizing non-orthogonality and quantum measurements, distinct from traditional features like entanglement. This approach ensures robustness and aligns with the quantum principles without needing to prove the quantum nature of non-orthogonality, as this is well-documented in the literature. - **Integration with Standard Protocols**: Our protocol can be used alongside standard QKD protocols, enhancing their performance through channel control and line tomography. Sections V and VI of this [paper](https://che01.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fabs%2F2308.03733&data=05%7C01%7Ckaran%40terraquantum.swiss%7Cea042cdd2aaa402fb9a008dbcf4d1c0a%7Ca29b5ad8d9e147ba97162ea42f6f9bd0%7C0%7C0%7C638331702314708440%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=KJOhdA9bkJGmyQIUdAXcYMEbip%2FjxCY9oBmxj1Xk5QA%3D&reserved=0) demonstrate this for the BB84 and Coherent One-Way protocols. - **Quantum vs. Classical**: It's simpler to assert that our protocol is "non-classical" rather than proving it's "quantum." Our solution relies on the collapse of the quantum wavefunction, a fundamental aspect of quantum mechanics. The well-understood mathematical theory of measuring quantum states, central to phenomena like Schrödinger's cat and Heisenberg's uncertainty principle, underpins our approach. - **Focus on Wavefunction Collapse**: Our most compelling argument lies in emphasizing the collapse of the quantum wavefunction, distinguishing our solution as both quantum and practical. For further reading, check out this [website](https://che01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fgerdbreitenbach.de%2Fgallery%2Fgalchap6.html&data=05%7C01%7Ckaran%40terraquantum.swiss%7Cea042cdd2aaa402fb9a008dbcf4d1c0a%7Ca29b5ad8d9e147ba97162ea42f6f9bd0%7C0%7C0%7C638331702314708440%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=vu%2FdPPoBTQfQ%2FEwaS4utgB2VkeLzNLzVaZooZZdlDEM%3D&reserved=0).