pdf/quantum-coherence-and-geometric-quantum-discord-5157tnq10j.pdf

Quantum coherence and geometric quantum discord

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott’s code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.

The SIC Question: History and State of Play

Resource theory is a widely applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this Letter, we propose a general scheme for analyzing resource theories based on resource destroying maps, which leave resource-free states unchanged but erase the resource stored in all other states. We introduce a group of general conditions that determine whether a quantum operation exhibits typical resource-free properties in relation to a given resource destroying map. Our theory reveals fundamental connections among basic elements of resource theories, in particular, free states, free operations, and resource measures. In particular, we define a class of simple resource measures that can be calculated without optimization, and that are monotone nonincreasing under operations that commute with the resource destroying map. We apply our theory to the resources of coherence and quantum correlations (e.g., discord), two prominent features of nonclassicality.

/pdf/resource-destroying-maps-4fj61l1uxt.pdf

Resource destroying maps

We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $$d$$d-dimensional bipartite and multipartite systems. The criterion for bipartite quantum states is effective in detecting several well-known classes of quantum states. For isotropic states, it becomes both necessary and sufficient. Furthermore, our criteria can be experimentally implemented, and the criterion for two-qudit states requires less local measurements than the one based on mutually unbiased measurements.

/pdf/general-sic-measurement-based-entanglement-detection-4br8i2uwew.pdf

General SIC measurement-based entanglement detection

We provide a detailed proof of an analytical lower bound of entanglement quantified by concurrence for arbitrary bipartite quantum states. It is shown that though the bound does not allow one to detect bound entanglement, it is tight for some mixed states and can detect most of the free entanglement. On the other hand, it is known that the entanglement monogamy inequality proposed by Coffman, Kundu, and Wootters is, in general, not true for higher-dimensional quantum states. Inducing from the lower bound of concurrence, we find a proper form of entanglement monogamy inequality for arbitrary pure quantum states.

Proper monogamy inequality for arbitrary pure quantum states (4 pages)

In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their respectively classical counterparts. Along the way, we propose a variational quantum generalized eigenvalue solver that finds the generalized eigenvalues and eigenstates of a matrix pencil $(\mathcal{G},\mathcal{S})$. As a proof of principle, we implement our algorithm to solve ${2}^{5}\ifmmode\times\else\texttimes\fi{}{2}^{5}$ generalized eigenvalue problems. Finally, our results offer two optional outputs with quantum or classical form, which can be directly applied in another quantum or classical machine learning process.

pdf/variational-quantum-algorithms-for-dimensionality-reduction-3is7wfoexj.pdf

Variational quantum algorithms for dimensionality reduction and classification

In this review, we introduce well-known Bell inequalities, the relations between the Bell inequality and quantum separability, and the entanglement distillation of quantum states It is shown that any pure entangled quantum state violates one of Bell-like inequalities Moreover, quantum states that violate any one of these Bell-like inequalities are shown to be distillable New Bell inequalities that detect more entangled mixed states are also introduced

https://link.springer.com/content/pdf/10.1007%2Fs11434-011-4395-1.pdf

Bell inequality, separability and entanglement distillation

We study the entanglement of formation for arbitrary-dimensional bipartite mixed unknown states Experimentally measurable lower and upper bounds for entanglement of formation are derived

Measurable bounds for entanglement of formation

Variational quantum algorithms for trace norms and their applications

Entanglement of formation is an important measure of quantum entanglement. We present an experimental way to measure the entanglement of formation for arbitrary dimensional pure states. The measurement only evolves local quantum mechanical observables.

Method for measuring the entanglement of formation for arbitrary-dimensional pure states

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