1ICTQT, Đại học Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Ba Lan
2Department of Mathematics & Statistics, University of Calgary, Canada
3Institute for Quantum Science and Technology, University of Calgary, Canada
4Công ty TNHH điện toán lượng tử Cambridge
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Tóm tắt
A reconstruction of quantum theory refers to both a mathematical and a conceptual paradigm that allows one to derive the usual formulation of quantum theory from a set of primitive assumptions. The motivation for doing so is a discomfort with the usual formulation of quantum theory, a discomfort that started with its originator John von Neumann.
We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing that the conceptual backbone of quantum theory concerns the manner in which systems and processes compose.
Aside from the diagrammatic form, the key novel aspect of this reconstruction is the introduction of a new postulate, symmetric purification. Unlike the ordinary purification postulate, symmetric purification applies equally well to classical theory as well as quantum theory. Therefore we first reconstruct the full process theoretic description of quantum theory, consisting of composite classical-quantum systems and their interactions, before restricting ourselves to just the ‘fully quantum’ systems as the final step.
We propose two novel alternative manners of doing so, ‘no-leaking’ (roughly that information gain causes disturbance) and ‘purity of cups’ (roughly the existence of entangled states). Interestingly, these turn out to be equivalent in any process theory with cups & caps. Additionally, we show how the standard purification postulate can be seen as an immediate consequence of the symmetric purification postulate and purity of cups.
Other tangential results concern the specific frameworks of generalised probabilistic theories (GPTs) and process theories (a.k.a. CQM). Firstly, we provide a diagrammatic presentation of GPTs, which, henceforth, can be subsumed under process theories. Secondly, we argue that the ‘sharp dagger’ is indeed the right choice of a dagger structure as this sharpness is vital to the reconstruction.
Featured image: Diagrammatic representation of the symmetric purification postulate.
Tóm tắt phổ biến
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Trích dẫn
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[6] David Schmid, John H. Selby, Matthew F. Pusey và Robert W. Spekkens, “Một định lý cấu trúc cho các mô hình bản thể luận tổng quát-phi ngữ cảnh”, arXiv: 2005.07161.
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[25] John H. Selby and Jamie Sikora, “How to make unforgeable money in generalised probabilistic theories”, arXiv: 1803.10279.
[26] Kenji Nakahira, “Derivation of quantum theory with superselection rules”, Đánh giá vật lý A 101 2, 022104 (2020).
[27] Arthur J. Parzygnat and Benjamin P. Russo, “A non-commutative Bayes’ theorem”, arXiv: 2005.03886.
[28] Łukasz Czekaj, Ana Belén Sainz, John Selby, and Michał Horodecki, “Correlations constrained by composite measurements”, arXiv: 2009.04994.
[29] Jacques Pienaar, “Quantum causal models via QBism: the short version”, arXiv: 1807.03843.
[30] John H. Selby và Ciarán M. Lee, "Các lý thuyết nguồn lực tổng hợp về sự gắn kết", arXiv: 1911.04513.
[31] Augustin Vanrietvelde, Hlér Kristjánsson, and Jonathan Barrett, “Routed quantum circuits”, arXiv: 2011.08120.
[32] Bob Coecke, Dominic Horsman, Aleks Kissinger và Quanlong Wang, “Sinh viên tốt nghiệp cơ học lượng tử Kindergarden (… hoặc cách tôi học cách ngừng dán LEGO lại với nhau và yêu thích phép tính ZX)”, arXiv: 2102.10984.
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[35] Abraham Westerbaan, Bas Westerbaan, and John van de Wetering, “Pure Maps between Euclidean Jordan Algebras”, arXiv: 1805.11496.
[36] John van de Wetering, “Lý thuyết lượng tử từ các nguyên tắc, Phần mềm lượng tử từ các sơ đồ”, arXiv: 2101.03608.
[37] Paulo J. Cavalcanti, John H. Selby, Jamie Sikora, Thomas D. Galley, and Ana Belén Sainz, “Witworld: A generalised probabilistic theory featuring post-quantum steering”, arXiv: 2102.06581.
[38] Lucien Hardy, “Time Symmetry in Operational Theories”, arXiv: 2104.00071.
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Không thể tìm nạp Crossref trích dẫn bởi dữ liệu trong lần thử cuối cùng 2021 / 04-28 10:57:14: Không thể tìm nạp dữ liệu được trích dẫn cho 10.22331 / q-2021 / 04-28-445 từ Crossref. Điều này là bình thường nếu DOI đã được đăng ký gần đây.
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