Quantum measurements: status and problems

1. Quantum measurements: status and problems Michael B. Mensky P.N.Lebedev Physical Institute Moscow, Russia MARKOV READINGSMoscow, May 12, 2005

2. Quantum Gravity and Quantum Measurements • M.A.Markov on Qu Meas Nature of physical knowledge (1947) Three interpretations of QM (1991) M.A.Markov and Bryce DeWitt 3d Intern. Seminar on Quantum Gravity Moscow, 1984

3. Message of the talk • Physics of Qu Meas: • Entanglement ( Qu Informatics) • Phenomenology of Qu Meas: • Open quantum systems and decoherence • Meta-physics of Qu Meas: • Everett’s interpretation and consciousness

4. Plan of the talk • Physics: Entanglement and decoherence • Continuous measurements: open quantum systems and dissipation • Quantum informatics • Bell’s theorem • Conceptual problems (M.A.Markov 1947) • Everett interpretation (M.A.Markov 1991)

5. Literature on decoherence • H.D.Zeh,Found. Phys. 1, 69 (1970); 3, 109 (1973) • W.H.Zurek,Phys. Rev. D 24, 1516 (1981); D 26, 1862 (1982) • D.Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, & H.D. Zeh,Decoherence and the appearance of a classical world in quantum theory, Springer, Berlin etc., 1996 M.M.

6. Reduction postulate • Von Neumann reduction postulate |=c1|a1+ c2|a2 |a1, p1=| c1 |2  |a2, p2=| c2 |2 • With projectors P1 = |a1  a1| , P2 = |a2  a2| |  P1 | , p1=| P1 |  P2 | , p2=| P2 |

7. Generalization of reduction postulate • Many alternatives( Pi = 1)i |  Pi| , pi=| Pi| • Fuzzy measurement(dxRx†Rx = 1) x |  Rx| , p(x) =| Rx†Rx|

8. Open systems andcontinuous measurements • Decoherence and dissipation from interaction with environment Measurement (phenomenology) Environment System System • Open quantum systems • = continuously measured ones

9. Entanglement • Measuring as an interaction: evolutionU |a1|0 U|a1|0 = |a1 |1 |a2|0 U|a2|0 = |a2 |2 • Entanglement ||0 = (c1|a1+c2|a2)|0 = c1|a1|0+c2|a2|0  U(c1|a1|0+c2|a2|0) = c1|a1|1+c2|a2|2 Entangled state

10. Decoherence • Entanglement |0  = | |0 = (c1|a1+ c2|a2) |0 c1|a1|1 + c2|a2|2 = | • Decoherence 0 = | | = (c1|a1+ c2|a2) (c1 a1|+ c2 a1|)  = Tr | | = |c1|2 |a1  a1| + |c2|2 |a2  a2| Reduction interpretated

11. Irreversible and reversible decoherence • Macroscopic uncontrollable environment  practically irreversible decoherence Environment Reservoir Meter System • Microscopic or mesoscopic environment  reversible decoherence info Meter System deco Reversion: U U-1

12. Restricted Path Integrals (RPI) • Continuous measurements presented by RPI • Monitoring an observable  decoherence • Non-minimally disturbing monitoring  dissipation

13. Restricted Path Integral: the paths, compatible with the readout Partial propagator: Uta(q'',q') = =d[p]d[q] wa[p,q] exp{(i/ћ) 0t (p dq - H dt)} Restricting Feynman path integral  q q” q’ t Weight functional Evolution: |ta= Uta |0, ta = Uta0(Uta)†

14. Effective Schroedinger equation • Restricted Path Integral for monitoring A Ut[a](q'',q')=d[p]d[q] exp{(i/ћ)0t(p dq - H dt) - 0t[A(t) - a(t)]2dt} • Effective Hamiltonian  H[a] (p,q,t) = H(p,q,t) - i ћ(A(p,q,t) - a(t))2 • Effective Schroedinger equation |t[a]/t = [- (i/ћ) H - (A - a(t))2]|t[a] Imaginary potential

15. Dynamical role of information • Von Neumann's projection: final state depends on the information • RPI: projecting process • Dynamics of a measured system depends on the information escaping from it • The role for quantum informatic devices: the processed information not escaping

16. Quantum informatics • Qubits • Quantum computer • Quantum cryptography • Quantum teleportation

17. Qubits • Two-level system |0, |1 • Superposition a|0+ b |1 •  quantum parallelism (entangled states) (|0+ |1)2 = |00+ |01 + |10 + |11 (|0+ |1)N = 02N-1|x

18. Quantum computer • Quantum parallelism (|0+ |1)N = 02N-1|x • Calculation time tP(N) instead of teN • Quantum algorithms • Factorization in prime numbers = finding the period of a periodic function (digital Fourier decomposition)  Cryptography

19. Quantum cryptography • Quantum cloning ||A | | |A’ impossible |1|A |1 |1 |A1, |2|A |2 |2 |A2 Linearity:(|1+ |2)|A (|1 |1+|2 |2) |A’’ not (|1 |1+|2 |2+|1 |2+|2 |1)|A’’ • Sequence of states: |1 |0 |1...|1 Eavesdropping discovered (|0 and|1 non-orthogonal) • Distribution of code sequences (factorization in prime numbers used)

20. Quantum teleportation • Correlation takes no time (pre-arranged) • Communication with light speed Meas Result i A B |A = a|0+ b |1 | B  Ui | B = |B Meas | A Qu correlation (entanglement)

21. Bell’s theorem • EPR effect • Local realism • Bell’s inequality • Aspect’s experiment

22. EPR effect S=0 • Maximal entanglement: | | - | | =|A+1|A-2 - |A-1| A+2 anticorrelation of spin projections •  Correlation of projections on different axes S=1/2 S=1/2

23. Local realism • Anticorrelation: |A+1|A-2 - |A-1| A+2 • Assumtion of local realism means: • If |A-2, then really|A+1 • If | A+2, then really|A-1 • Then measurement is interpreted as |Am1| Bn2  |Am1| B-n1(same particle)

24. Bell inequality • Given P(A± B± C±) for a single particle and local realism • From probability sum rule: P(A- B+) = P(A- B+ C+) + P(A- B+ C-) P(A+ C-) = P(A+ B+ C-) + P(A+ B- C-) P(B+ C-) = P(A+ B+ C-) + P(A- B+ C-) • Bell inequality: P(A- B+) + P(A+ C-)  P(B+ C-)

25. Realism refuted • Local realism  Bell inequality • Aspect: Bell inequality is violated •  No local realism in Qu Mechanics • Properties found in a measurement do not exist before the measurement

26. Conceptual problems • Paradoxes: Schroedinger cat etc. • No reality previous to measurement • Linear evolution c1|a1|0+c2|a2|0 c1|a1|1+c2|a2|2  reduction impossible

27. Everett interpretation • Linear evolution c1|a1|0+c2|a2|0 c1|a1|1+c2|a2|2 • Many classical realities (many worlds) • Selection = consciousness

28. Quantum consciousness • Qu world = many classical realities • Consciousness = Selection Consciousness = selection of a class. reality Unconsciousness = all class. realities = qu world • At the edge of consciousness (trance) Choice of reality (modification of probabilities) Contact with the quantum world (other realities)

29. Conclusion • Physics of measurements: entanglement • Open systems = continuously measured ones • Entanglement Quantum informatics • Conceptual problems: no selection in QM • Everett: Selection = consciousness • Quantum consciousness: choice of reality etc.

30. Обзоры • M.M.,Квантовая механика и декогеренция, Москва, Физматлит, 2001 [translated from English (Quantum Measurements and Decoherence, Kluwer, Dordrecht etc., 2000)] • M.M.,Диссипация и декогеренция квантовых систем, УФН 173, 1199 (2003)[Physics-Uspekhi 46, 1163 (2003)] • M.M., Понятие сознания в контексте квантовой механики,УФН 175, 413 (2005)[Physics-Uspekhi 175 (2005)

31. Conceptual problems of QuantumMechanics • M.M., Quantum mechanics: New experiments, new applications and new formulations of old questions, Physics-Uspekhi 43, 585-600 (2000). [Russian: М.М., УФН 170, 631 (2000)] • М.М., Conception of consciousness in the context of quantum mechanics, Physics-Uspekhi 175, No.4 (2005)] [Russian: М.М., 175, 413 (2005)]

32. Sections of the Talk • Introduction • Op en systems and continuous measurements • Restricted Path Integrals (RPI) • Non-minimally disturbing monitoring • Realization by a series of soft observations • Conclusion and reviews