Quantum measurements status and problems
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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 = Uta0(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 tP(N) instead of teN

  • 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

    |Am1| Bn2  |Am1| B-n1(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


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