An introduction to entanglement measures.

An introduction to entanglement measures.

10 Jun 2006 | Martin B. Plenio and Shashank Virmani
This review presents an overview of entanglement measures, focusing on the finite-dimensional two-party case. It covers key concepts such as single-copy and asymptotic entanglement manipulation, entanglement of formation, entanglement cost, distillable entanglement, relative entropic measures, squashed entanglement, log-negativity, robustness monotones, and the greatest cross-norm. The paper also briefly discusses infinite-dimensional systems and multi-party settings. Entanglement is a fundamental resource in quantum information science, enabling tasks that are impossible or inefficient in the classical realm. The review emphasizes the importance of quantifying entanglement, which involves characterizing, manipulating, and measuring entangled states. The paper discusses the LOCC (Local Operations and Classical Communication) paradigm, which is central to understanding entanglement as a resource. It explains that entanglement is the quantum correlations that cannot be simulated classically and that LOCC operations are essential for quantum information protocols. The paper introduces the concept of entanglement measures, which are mathematical quantities that quantify the amount of entanglement in a quantum state. It discusses the properties that a good entanglement measure should satisfy, including monotonicity under LOCC operations, convexity, and additivity. The review also presents several important entanglement measures, such as the entanglement cost, distillable entanglement, and the entropy of entanglement. These measures are essential for understanding the behavior of entangled states under various quantum operations and for developing quantum information protocols. The paper highlights the importance of entanglement in quantum information science, emphasizing its role in quantum communication, quantum computing, and quantum cryptography. It discusses the challenges in quantifying entanglement, particularly in multi-party systems, and the significance of entanglement measures in addressing open questions in quantum information theory. The review concludes by emphasizing the need for further research into entanglement measures and their applications in quantum information science.This review presents an overview of entanglement measures, focusing on the finite-dimensional two-party case. It covers key concepts such as single-copy and asymptotic entanglement manipulation, entanglement of formation, entanglement cost, distillable entanglement, relative entropic measures, squashed entanglement, log-negativity, robustness monotones, and the greatest cross-norm. The paper also briefly discusses infinite-dimensional systems and multi-party settings. Entanglement is a fundamental resource in quantum information science, enabling tasks that are impossible or inefficient in the classical realm. The review emphasizes the importance of quantifying entanglement, which involves characterizing, manipulating, and measuring entangled states. The paper discusses the LOCC (Local Operations and Classical Communication) paradigm, which is central to understanding entanglement as a resource. It explains that entanglement is the quantum correlations that cannot be simulated classically and that LOCC operations are essential for quantum information protocols. The paper introduces the concept of entanglement measures, which are mathematical quantities that quantify the amount of entanglement in a quantum state. It discusses the properties that a good entanglement measure should satisfy, including monotonicity under LOCC operations, convexity, and additivity. The review also presents several important entanglement measures, such as the entanglement cost, distillable entanglement, and the entropy of entanglement. These measures are essential for understanding the behavior of entangled states under various quantum operations and for developing quantum information protocols. The paper highlights the importance of entanglement in quantum information science, emphasizing its role in quantum communication, quantum computing, and quantum cryptography. It discusses the challenges in quantifying entanglement, particularly in multi-party systems, and the significance of entanglement measures in addressing open questions in quantum information theory. The review concludes by emphasizing the need for further research into entanglement measures and their applications in quantum information science.
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[slides and audio] An introduction to entanglement measures