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QCrypt 2013, Waterloo, Canada, Aug. 9 2013

The Structure of a world (which may be) described by quantum mechanics A. J. Leggett Department of Physics, University of Illinois at Urbana-Champaign Institute for Quantum Computing, University of Waterloo Support: John D. and Catherine T. Macarthur Foundation John Templeton Foundation.

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QCrypt 2013, Waterloo, Canada, Aug. 9 2013

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  1. The Structure of a world (which may be) described by quantum mechanicsA. J. LeggettDepartment of Physics, University of Illinois at Urbana-ChampaignInstitute for Quantum Computing, University of WaterlooSupport: John D. and Catherine T. Macarthur Foundation John Templeton Foundation QCrypt 2013, Waterloo, Canada, Aug. 9 2013

  2. The structure of a world described by quantum mechanics Theoretical account of the world given by quantum mechanics (QM) is very bizarre. But, a theory is only as good as the experiments which support it. So:What can we infer about the nature/structure of the physical world • from existing experiments which test QM • on the assumption that all future experiments will confirm predictions of QM? Two major areas of experimentation: • EPR-Bell • Schrödinger’s cat Both (may) involve in their interpretation the concept of realism. So: what do we (can we) mean by “realism” in physics?

  3. “Realism” in the simplest case: a two state system (Microscopic) example: photon polarization “Question” posed to photon:Are you polarized along a? (“A = +1”) Or perpendicular to a? (“A = -1”) Experimental fact: For each photon, either counter Y clicks (and counter N does not) or N clicks (and Y does not). Natural “paraphrase”:When asked, each photon answers either “yes” (A = +1) or “no” (A = -1). But: what if it is not asked? (no measuring device…) Single (heralded) photon Single (heralded) photon Detector Polarizer with transmission axis‖ to a Macroscopicevents

  4. Macroscopic counterfactual definiteness (MCFD) Suppose a given photon is directed “elsewhere”.What does it mean to ask “does it have a definite value of A?”? A possible quasi-operational definition:Suppose photon had been switched into measuring device:Then:Proposition I (truism?): It is a fact that either counter Y would have clicked (A = +1) or counter N would have clicked (A = -1).Proposition II (MCFD): Either it is a fact that counter Y would have clicked (i.e. it is a fact that A = +1) or it is a fact that counter N would have clicked (A = -1). Do counterfactual statements have truth values?(common sense, legal system…assume so!) “Elsewhere” Single (heralded) photon Switch ⇓ ? Microrealism ⇒ MCFD ⇒

  5. The EPR-Bell experiments (idealized) CHSH inequality: all objective local theories (OLT’s) satisfy the constraints (✱) (✱) is violated by predictions of QM, and by experimental data. (⬆: “loopholes” – individually blocked except for “collapse locality” loophole: at what point is a definite outcome “realized”?) atomic source randomlyactivatedswitch ( , etc.)

  6. The EPR-Bell experiments (cont.) Thus, modulo “loopholes”, all OLT’s are refuted by experiment. Defining postulates of an OLT: conjunction of • Induction ( standard “arrow of time”) • Einstein locality (no superluminal causality) • Microrealism/MCFD Can we do without 3)? (i.e. are 1) and 2) alone sufficient to prove CHSH theorem?) Involves v. delicate questions concerning definition of probability… Anyway, irrespective of this, existing experiments prima facie imply at least one of 1) – 3) has to go. ⬆: What about “collapse locality” loophole? Maybe in future: long-baseline EPR-Bell experiment. Until then, what can we say about the process (?) of “collapse” (“realization”)? Note existence of alternative (non-QM) scenarios (CSL, Penrose…) ⇒ Can we build Schrödinger’s Cat in the lab? Nb: 2) ⇒ 1)in SR but not necessarily in more general theory

  7. Can we prove CHSH theorem without invoking realism/MCFD? (e.g. N. Gisin, Found. Phys.42, 80 (2012)) ⇒ CHSH inequality ⬆: Problem: What does p(a|x,Y) actually mean?e.g. if Y represents a standard “hidden variable”:if values of Y are discrete and finite in number, can use “frequentist” df.: But: what if Y is a continuous variable/state description? “state of universe” measured correlation “probability of Alice’s outcome agiven setting x and state Y”

  8. Macroscopic quantum coherence (MQC) time “Q = +1” “Q = -1” macroscopicallydistinct states Example: “flux qubit” Existing experiments: if raw data interpreted in QM terms, state at tint is quantum superposition (not mixture!) of states (+) and (--). ⬆: how “macroscopically” distinct? Supercond. ring Josephson junction “Q= +1” “Q= -1” tint tf ti

  9. How “macroscopically distinct” are (notionally) superposed states of flux qubit? Korsbakkenet al. (EPL 89, 30003 (2010)): Q: How many single electrons do we need to displace to go from +I to –I? (ans. = “W”) Ans.: for all flux-qubitexpts. to date,“not macroscopic or even mesoscopic”. Well, maybe… Q: What is W? A: If we work in terms of indl. “elementary” particles (inc. nucleons not nuclei!),If we consider nuclei as “elementary”, then WDP ~ 105. However, if we do so, then in the flux qubit case we should consider Cooper pairs as “elementary” ⇒ WFQ ~ 106 – 107 ⇒ either way, states of flux qubit are more “macroscopically distinct” than those of dust particle! dust particle +I –I

  10. MQC (cont.) Analog of CHSH theorem for MQC:Any macrorealistictheory satisfies constraint which is violated (for appropriate choices of the ti) by the QM predictions for an “ideal” 2-state system Definition of “macrorealistic” theory: conjunction of • induction • macrorealism(Q(t) = +1 or-1 for all t) • noninvasive measurability (NIM) NIM: If Q = +1, throw away If Q = -1, keep In this case, unnatural to assert 2) while denying 3). NIM cannot be explicitly tested, but can make “plausible” by ancillary experiment to test whether, when Q(t) is known to be (e.g.) +1, a noninvasive measurement does or does not affect subsequent statistics. But measurements must be projective (“von Neumann”). Existing experiments use “weak-measurement” techniques (and arguable whether states macroscopically distinct). measuring device

  11. Conclusions • From existing EPR-Bell experiments, must either • reject at least one of induction locality MCFD • invoke collapse locality loophole. • If future long-baseline experiment verifies QM predictions, • is unviable. • If a future MQC experiment with v. N. measurements verifies QM predictions, must reject at least one of inductionmacrorealism NIM • If result of 3. is QM’l but that of 2. not, raises question:Are human “observers” special?(Wigner’s friend: UIUC experiment) A final thought: is induction (“arrow of time”) sacred? macroscopic counterfactual definiteness non-invasive measurability

  12. QM of human vision Methods: • Two conditions • Superposition condition: N photons at (L) +(R) state • Mixed condition: N photons each at (L) or (R) with equal probability • Observer judges whether a light was present on Left and on Right separately • Data analysis • If the detection rates at L and/or R in the superposition condition is statistically different from that of the mixed condition, then QM is violated. or Mixed condition Superposition condition

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