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1. Quantum State Combinatorics

   https://doi.org/10.3390/e26090764  

   Scholes, Gregory D (September 2024, Entropy)

   This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations for the complex structure of non-classical multipartite correlations with surprisingly little information about the state. We show, with pegagogical examples, how known results from combinatorics can be used to reveal the expected structure of various correlations hidden in the ensemble described by a state. 

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2. A molecular perspective on quantum information

   https://doi.org/10.1098/rspa.2023.0599  

   Scholes, Gregory D. (November 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Some of the fundamentals of quantum information science are described, including the concepts of quantum resources, quantum states and mixedness of states. The explanations are detailed and include a combination of basic facts with fully worked examples, and some more advanced topics. The principles of quantum information are illustrated with chemical examples drawn from singlet fission, photophysics of radicals, molecular excitons, electron transfer and so on. Suggestions for prospects and challenges for the field are discussed. 

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3. Quantum nondemolition measurements with optical parametric amplifiers for ultrafast quantum information processing

   https://doi.org/10.1364/CLEO_FS.2023.FTu3A.2  

   Yanagimoto, Ryotatsu; Nehra, Rajveer; Hamerly, Ryan; Ng, Edwin; Marandi, Alireza; Mabuchi, Hideo (January 2023, Optica Publishing Group)

   We show that quantum nondemolition measurements using an optical parametric amplifier can be a universal tool for ultrafast quantum information processing, enabling, photon-number-resolving measurements and deterministic generation of Gottesman-Kitaev-Preskill (GKP) states. 

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4. Cutoff phenomenon and entropic uncertainty for random quantum circuits

   https://doi.org/10.1088/2516-1075/acf2d3  

   Oh, Sangchul; Kais, Sabre (September 2023, Electronic Structure)

   Abstract How fast a state of a system converges to a stationary state is one of the fundamental questions in science. Some Markov chains and random walks on finite groups are known to exhibit the non-asymptotic convergence to a stationary distribution, called the cutoff phenomenon. Here, we examine how quickly a random quantum circuit could transform a quantum state to a Haar-measure random quantum state. We find that random quantum states, as stationary states of random walks on a unitary group, are invariant under the quantum Fourier transform (QFT). Thus the entropic uncertainty of random quantum states has balanced Shannon entropies for the computational basis and the QFT basis. By calculating the Shannon entropy for random quantum states and the Wasserstein distances for the eigenvalues of random quantum circuits, we show that the cutoff phenomenon occurs for the random quantum circuit. It is also demonstrated that the Dyson-Brownian motion for the eigenvalues of a random unitary matrix as a continuous random walk exhibits the cutoff phenomenon. The results here imply that random quantum states could be generated with shallow random circuits. 

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5. Quantum optical memory for entanglement distribution

   https://doi.org/10.1364/OPTICA.493732  

   Lei, Yisheng; Kimiaee Asadi, Faezeh; Zhong, Tian; Kuzmich, Alex; Simon, Christoph; Hosseini, Mahdi (January 2023, Optica)

   Optical photons are powerful carriers of quantum information, which can be delivered in free space by satellites or in fibers on the ground over long distances. Entanglement of quantum states over long distances can empower quantum computing, quantum communications, and quantum sensing. Quantum optical memories are devices designed to store quantum information in the form of stationary excitations, such as atomic coherence, and are capable of coherently mapping these excitations to flying qubits. Quantum memories can effectively store and manipulate quantum states, making them indispensable elements in future long-distance quantum networks. Over the past two decades, quantum optical memories with high fidelities, high efficiencies, long storage times, and promising multiplexing capabilities have been developed, especially at the single-photon level. In this review, we introduce the working principles of commonly used quantum memory protocols and summarize the recent advances in quantum memory demonstrations. We also offer a vision for future quantum optical memory devices that may enable entanglement distribution over long distances. 

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