Schmidt Decomposition and Coherence of Interfering Alternatives

Fastovets, D. V.; Bogdanov, Yu. I.; Богданова, Н. А.; Лукичев, В. Ф.

doi:10.1134/s1063739721040065

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…It imposes a practical limit on applications that require high-resolution images. Attempts to improve and enhance image quality and resolution focused on employing a pseudo-inverse ghost imaging technique via a sparsity constraint [47], employing a Schmidt decomposition for image enhancement [48], and imaging based on Fourier spectrum acquisition [49].…”

Section: ) Quantum Magnetometry and Magnetoelectricity Empirical Resultsmentioning

confidence: 99%

Exploring Quantum Sensing Potential for Systems Applications

et al. 2023

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The current rise of quantum technology is compelled by quantum sensing research. Thousands of research labs are developing and testing a broad range of sensor prototypes. However, there is a lack of knowledge about specific applications and real-world use cases where the benefits of these sensors will be most pronounced. This study presents a comprehensive review of quantum sensing state-of-practice. It also provides a detailed analysis of how quantum sensing overcomes the existing limitations of sensordriven systems' precision and performance. Based on the review of over 500 quantum sensor prototype reports, we determined four groups of quantum sensors and discussed their readiness for commercial usage. We concluded that quantum magnetometry and quantum optics are the most advanced sensing technologies with empirically proven results. In turn, quantum timing and kinetics are still in the early stages of practical validation. In addition, we defined four systems domains in which quantum sensors offer a solution for existing limitations of conventional sensing technologies. These domains are 1) GPS-free positioning and navigating services, 2) time-based operations, 3) topological visibility, and 4) environment detection, prediction, and modeling. Finally, we discussed the current constraints of quantum sensing technologies and offered directions for future research.

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Section: ) Quantum Magnetometry and Magnetoelectricity Empirical Resultsmentioning

confidence: 99%

Exploring Quantum Sensing Potential for Systems Applications

et al. 2023

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“…In summary, Table 2 provides a comparative analysis of quantum encoding techniques in terms of mathematical forms, number of qubits, runtime complexity, and applications. However, note that there are several other encoding patterns that exist, e.g., space encoding [66], matrix or dynamic encoding [83], Schmidt decomposition [130], instantaneous quantum polynomial (IQP) style encoding [131], Schrödinger's cat code encoding [132], QAOA ansatz encoding [133], time-bin encoding [134], parity encoding [135], arbitrary continuous-variable encoding [136], Fock encoding and coherent-state encoding schemes [137], etc.…”

Section: H Hamiltonian Evolution Ansatz Encodingmentioning

confidence: 99%

Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing

Khan,

Aman,

Sikdar

2024

IEEE Access

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The existing body of research on quantum embedding techniques is not only confined in scope but also lacks a comprehensive understanding of the intricacies of the quantum embedding process. To address this critical issue, this article explores quantum encoding schemes, uncovering valuable insights into their encoding algorithms from theoretical foundations to a mathematical perspective, as well as practical applications. Initially, the article briefly overviews classical computing and the limitations associated with classical bits in representing and processing complex information. Next, the article scrutinizes a variety of quantum embedding patterns, including basis encoding, amplitude encoding, Qsample encoding, angle encoding, quantum associative memory encoding, quantum random access memory, superdense encoding, Hamiltonian encoding, and others. In addition, each technique is accompanied by mathematical formulas and examples illustrating how each strategy can be applied. Finally, the article provides a comparative analysis of different quantum embedding/encoding methods, outlining their strengths and limitations. Overall, this insightful article highlights the potential of quantum encoding techniques for efficient information processing beyond classical bits, thereby facilitating scientists and design engineers in selecting the most appropriate encoding technique to develop smart algorithms for revolutionizing the field of quantum computing.INDEX TERMS Encoding patterns, qubits, quantum computing, quantum information processing, quantum circuits.

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“…It is surprising that in the literature, when multimode (with D > 2 modes) systems are considered, the only studied cat states are the ones associated to the total parity subgroup Z 2 ⊂ Z D−1 2 (the one formed by the parity transformations in Eqns. ( 15)-( 16), see for instance [50,51]. However, there are models, like the D-level LMG model, where the Hamiltonian is invariant under parity transformations, where the lowest energy eigenstate and some of the first excited states are parity adapted CS.…”

Section: Lmg D-level Modelmentioning

confidence: 99%

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

Guerrero¹,

Sojo²,

Mayorgas³

et al. 2023

Preprint

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In this paper we study the entanglement in symmetric N -quDit systems. In particular we use generalizations to U (D) of spin U (2) coherent states and their projections on definite parity c ∈ Z D−1 2 (multicomponent Schrödinger cat) states and we analyse their reduced density matrices when tracing out M < N quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to proof a theorem for the decomposition of a N -quDit Schrödinger cat state with a given parity c into a sum over all possible parities of tensor products of Schrödinger cat states of N − M and M particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit (N, M → ∞, M/N fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted coherent states of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

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Schmidt Decomposition and Coherence of Interfering Alternatives

Cited by 6 publications

References 28 publications

Exploring Quantum Sensing Potential for Systems Applications

Exploring Quantum Sensing Potential for Systems Applications

Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

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