{"product_id":"finite-and-profinite-quantum-systems-apostolos-vourdas-9783319594941","title":"Finite and Profinite Quantum Systems","description":"\u003cp\u003eThis monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics.\u003c\/p\u003e \u003cp\u003eThe first major part of this monograph studies the so-called  qubits' and  qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. \u003c\/p\u003e\u003cp\u003eThe second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers.\u003c\/p\u003e \u003cp\u003eApplications of the formalism include quantum optics and quantum computing, two-dimensional electron systems in magnetic fields and the magnetic translation group, the quantum Hall effect, other areas in condensed matter physics, and Fast Fourier Transforms.\u003c\/p\u003e The monograph combines ideas from quantum mechanics with discrete mathematics, algebra, and number theory. It is suitable for graduate students and researchers in quantum physics, mathematics and computer science.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Apostolos Vourdas\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 331959494X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783319594941\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/28\/2017\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 196\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.10lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.64h x 6.57w x 0.69d","brand":"Apostolos Vourdas","offers":[{"title":"Hardcover","offer_id":44540631089407,"sku":"9783319594941","price":89.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_395eeb52-2f5f-4932-8064-baddfa7dff6e.jpg?v=1700588988","url":"https:\/\/www.whiterainbookhouse.com\/products\/finite-and-profinite-quantum-systems-apostolos-vourdas-9783319594941","provider":"WR Book House","version":"1.0","type":"link"}