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Quantum measurements: status and problems. Michael B. Mensky P.N.Lebedev Physical Institute Moscow, Russia. MARKOV READINGS Moscow, May 12, 2005. Quantum Gravity and Quantum Measurements. M .A.Markov on Qu Meas Nature of physical knowledge (1947) Three interpretations of QM (1991).
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Quantum measurements: status and problems Michael B. Mensky P.N.Lebedev Physical Institute Moscow, Russia MARKOV READINGSMoscow, May 12, 2005
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
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
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)
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.
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 |
Generalization of reduction postulate • Many alternatives( Pi = 1)i | Pi| , pi=| Pi| • Fuzzy measurement(dxRx†Rx = 1) x | Rx| , p(x) =| Rx†Rx|
Open systems andcontinuous measurements • Decoherence and dissipation from interaction with environment Measurement (phenomenology) Environment System System • Open quantum systems • = continuously measured ones
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
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
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
Restricted Path Integrals (RPI) • Continuous measurements presented by RPI • Monitoring an observable decoherence • Non-minimally disturbing monitoring dissipation
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 = Uta0(Uta)†
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
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
Quantum informatics • Qubits • Quantum computer • Quantum cryptography • Quantum teleportation
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
Quantum computer • Quantum parallelism (|0+ |1)N = 02N-1|x • Calculation time tP(N) instead of teN • Quantum algorithms • Factorization in prime numbers = finding the period of a periodic function (digital Fourier decomposition) Cryptography
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)
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)
Bell’s theorem • EPR effect • Local realism • Bell’s inequality • Aspect’s experiment
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
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 |Am1| Bn2 |Am1| B-n1(same particle)
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-)
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
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
Everett interpretation • Linear evolution c1|a1|0+c2|a2|0 c1|a1|1+c2|a2|2 • Many classical realities (many worlds) • Selection = consciousness
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)
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.
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)
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)]
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