Quantum measurements status and problems
This presentation is the property of its rightful owner.
Sponsored Links
1 / 32

Quantum measurements: status and problems PowerPoint PPT Presentation


  • 69 Views
  • Uploaded on
  • Presentation posted in: General

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).

Download Presentation

Quantum measurements: status and problems

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Quantum measurements status and problems

Quantum measurements: status and problems

Michael B. Mensky

P.N.Lebedev Physical Institute

Moscow, Russia

MARKOV READINGSMoscow, May 12, 2005


Quantum measurements status and problems

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

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

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

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

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

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 and continuous measurements

Open systems andcontinuous measurements

  • Decoherence and dissipation from interaction with environment

Measurement (phenomenology)

Environment

System

System

  • Open quantum systems

  • = continuously measured ones


Entanglement

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

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

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

Restricted Path Integrals (RPI)

  • Continuous measurements

    presented by RPI

  • Monitoring an observable

     decoherence

  • Non-minimally disturbing monitoring

     dissipation


Restricting feynman path integral

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

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

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

Quantum informatics

  • Qubits

  • Quantum computer

  • Quantum cryptography

  • Quantum teleportation


Qubits

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 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 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

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

Bell’s theorem

  • EPR effect

  • Local realism

  • Bell’s inequality

  • Aspect’s experiment


Epr effect

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

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

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

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

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

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

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

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.


Quantum measurements status and problems

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

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

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


  • Login