A Geometry of entanglement and entropy (2402.15880v2)
Abstract: This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics. Our focus centers on the connection between entanglement, von Neumann entropy, a measure of the information content within quantum systems and the geometry of composite Hilbert spaces. We discuss various methods for quantifying and characterizing entanglement through a geometric perspective and elucidate how this connection unveils the nature of quantum entanglement, offering valuable insights into the underlying structure of quantum systems. This study underscores the significance of geometry as a key tool for understanding the rich landscape of quantum correlations and their implications across various domains of physics and information theory. An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.
- Erwin Schrödinger. 1.11 the present situation in quantum mechanics: A translation of schrödinger’s” cat paradox’* paper. 1980.
- Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47:777–780, May 1935.
- David Bohm. Quantum theory. Courier Corporation, 2012.
- Communication via one- and two-particle operators on einstein-podolsky-rosen states. Phys. Rev. Lett., 69:2881–2884, Nov 1992.
- Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys. Rev. Lett., 70:1895–1899, Mar 1993.
- Quantum communication. Nature photonics, 1(3):165–171, 2007.
- Quantum secret sharing. Phys. Rev. A, 59:1829–1834, Mar 1999.
- Quantum cryptography. Rev. Mod. Phys., 74:145–195, Mar 2002.
- A one-way quantum computer. Phys. Rev. Lett., 86:5188–5191, May 2001.
- Distributed quantum computing: a survey, 2022.
- Thermodynamics and the measure of entanglement. Phys. Rev. A, 56:R3319–R3321, Nov 1997.
- Are the laws of entanglement theory thermodynamical? Phys. Rev. Lett., 89:240403, Nov 2002.
- Entanglement theory and the second law of thermodynamics. Nature Physics, 4(11):873–877, 2008.
- No second law of entanglement manipulation after all. Nature Physics, jan 2023.
- Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using lagrange’s identity and wedge product. Quantum Information Processing, 16(5):1–15, 2017.
- Classification and quantification of entanglement through wedge product and geometry. Physica Scripta, 2022.
- Geometry of distributive multiparty entanglement in 4- qubit hypergraph states. IET Quantum Communication, 3(1):72–84, 2022.
- Permutation symmetric hypergraph states and multipartite quantum entanglement. International Journal of Theoretical Physics, 58:3927–3944, 2019.
- Quantifying parallelism of vectors is the quantification of distributed n-party entanglement. Journal of Physics A: Mathematical and Theoretical, 53(9):095301, 2020.
- Entanglement polygon inequality in qubit systems. New Journal of Physics, 20(6):063012, 2018.
- Generalized monogamy relations of concurrence for n𝑛nitalic_n-qubit systems. Phys. Rev. A, 92:062345, Dec 2015.
- Triangle measure of tripartite entanglement. Phys. Rev. Lett., 127:040403, Jul 2021.
- Observable estimation of entanglement for arbitrary finite-dimensional mixed states. Phys. Rev. A, 78:042308, Oct 2008.
- Dimensionally sharp inequalities for the linear entropy. Linear Algebra and its Applications, 584:294–325, 2020.
- Distributed entanglement. Phys. Rev. A, 61:052306, Apr 2000.
- Geometric genuine multipartite entanglement for four-qubit systems, 2023.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
