Some tough acts to follow

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Tyrone Banks
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1 Some tough acts to follow Irina Dumitru Markus Grassl Captain Larsson Huangjun Zhu Ingemar Bengtsson Marcus Appleby John DeBrota Niklas Johansson

2 Welcome to the Qplex Christopher A. Fuchs UMass Boston The kind of place where a QBist dreams of hanging out.

4 Andrei Khrennikov QTFT 05, Vӓxjӧ, Sweden Ruediger Schack Too much QBism! Hans Briegel Kristian Camilleri Jan Faye Christopher Fuchs And, Theodor Haensch, 005 Nobel laureate

6 ###bism: The (wrong) belief that QBism makes you more attractive to women.

7 ###bism: The (wrong) belief that QBism makes you more attractive to women. tombism: Belief that lectures on QBism can bore you to death.

9 The Ithaca Interpretation of Quantum Mechanics, 996

10 The Ithaca Interpretation of Quantum Mechanics, 996 The Pondicherry Interpretation of Quantum Mechanics, 999

11 The Ithaca Interpretation of Quantum Mechanics, 996 The Pondicherry Interpretation of Quantum Mechanics, 999 The Vӓxjӧ Interpretation of Quantum Mechanics, 00

12 The Ithaca Interpretation of Quantum Mechanics, 996 The Pondicherry Interpretation of Quantum Mechanics, 999 The Vӓxjӧ Interpretation of Quantum Mechanics, 00 The Anti-Vӓxjӧ Interpretation of Quantum Mechanics, 00

13 Theme of QB 06, Vӓxjӧ, Sweden

14 The Paradigm of Entanglement I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. --- Erwin Schrӧdinger

15 A Seemingly Very Different Paradigm

17 The Vӓxjӧ Interpretation Andrei Khrennikov

18 Edwin T. Jaynes, Our present QM formalism is a peculiar mixture describing in part laws of Nature, in part incomplete human information about Nature --- all scrambled up together by Bohr into an omelette that nobody has seen how to unscramble. Yet we think the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, we cannot know what we are talking about; it is just that simple.

19 E. T. Jaynes, The Present Goal of QBism Of course, the QM formalism also contains fundamentally important and correct ontological elements It seems that, to unscramble the epistemological probability statements from the ontological elements we need to find a different formalism, isomorphic in some sense but based on different variables; it was only through some weird mathematical accident that it was possible to find a variable ψ which scrambles them up in the present way.

22 What QBism Gets Instead of Amplitude Addition

23 Gelo Tabia s Optical Qubit SIC-POVM Phys. Rev. A 86, 0607 (0)

24 Ground Path --- i.e., identity before measurement Measmt 3 4

25 Another way to write the identity evolution: 3 4 / 3 / 3 / 6 / 3 / 6 /3

26 Ground Path --- i.e., identity followed by measurement 3 4 / 3 / 3 / 6 / 3 / 6 /3 Measmt In the vernacular, Interference

27 Sky Path --- which way information obtained, followed by measurement 3 4 / 3 / 3 / / 3 / 6 /3 Measmt Interference Disappears!

28 Least Negative Quasi-Probability Representation of QM Want to write the Born Rule as an analog of the Law of Total Probability: But cannot do it without introducing negative numbers in the summation (Feynman 98). That is, for any operator frame and its dual, At least some terms in the sum must be negative. Huangjun Zhu arxiv: So, what is the best possible frame?

29 Answer (H. Zhu, arxiv: ): On supposition that: A) is a self-dual frame B) Measure of negativity is worst case in sum. Then: for a SIC! (See also John DeBrota s talk, Thursday.)

30 Plugging in and simplifying, one obtains as before:

32 SIC Existence, the Latest Known: Exact solutions: d =, 4, 8, 3, 35, 37, 43 and 48 High precision numerical solutions, many to 8,000 and 6,000 digits accuracy: d =, 4, 43, 47, 68, 7, 95, 99, 8, 59, 33

35 That arena for developing quantum theory on QBist principles is the qplex (a notion we used to call a maximal consistent set )

36 (i.e., a qplex)

37 One Theorem from Our Upcoming Paper (D. M. Appleby, C. A. Fuchs, B. C. Stacey, H. Zhu) Theorem. The following statements are equivalent: A qplex is isomorphic to the quantum state space of a d-level system. The symmetry group of a qplex over d outcomes is the projective unitary group. A SIC exists in dimension d.

38 The Linkӧping Challenge: Might quantum state space simply correspond to a qplex of maximum Euclidean volume? I.e., full stop. No further assumptions! Who among us is brave enough to prove it?

Quantum Theory in a New Frame

Quantum Theory in a New Frame Christopher A. Fuchs Perimeter Institute for Theoretical Physics Waterloo, Canada Quantum Mechanics: The Axioms and Our Imperative! States correspond to density operators