Quantum measurements:

status and problems

Michael B. Mensky

P.N.Lebedev Physical Institute

Moscow, Russia

MARKOV READINGSMoscow, May 12, 2005

12.05.2005 2

M.A.Markov and Bryce DeWitt3d Intern. Seminar on Quantum Gravity

Moscow, 1984

Quantum Gravity and Quantum Measurements

• M.A.Markov on Qu MeasNature of physical knowledge (1947)

Three interpretations of QM (1991)

12.05.2005 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

12.05.2005 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)

12.05.2005 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.

12.05.2005 6

Reduction postulate

• Von Neumann reduction postulate

c1|a1+ c2|a2 |a1 p1=| c1 |2

|a2 p2=| c2 |2

• With projectors P1 = |a1 a1P2 = |a2 a2 P1 p1=P1

P2 p2=P2

12.05.2005 7

Generalization of reduction postulate

• Many alternatives ( Pi = 1) i Pi pi =Pi

• Fuzzy measurement (dx Rx† Rx = 1)

x Rx p(x) =Rx

† Rx

12.05.2005 8

Open systems and continuous measurements

• Decoherence and dissipation from interaction with environment

System

System

EnvironmentMeasurement

(phenomenology)

• Open quantum systems = continuously measured ones

12.05.2005 9

• Measuring as an interaction: evolution U

|a10 U |a10|a1

|a20 U |a20|a2• Entanglement

c1|a1+c2|a20c1|a10+c2|a20

U c1|a10+c2|a20c1|a1+c2|a2

Entanglement

Entangled state

12.05.2005 10

• Entanglement

c1|a1+ c2|a20

c1|a1+ c2|a2• Decoherence

0 = c1|a1+ c2|a2 c1a1| + c2a1| Tr|c1|2 |a1a1|c2|2 |a2a2

Decoherence

Reduction interpretated

12.05.2005 11

Irreversible and reversible decoherence

System

System

ReservoirMeter

Meterinfo

deco

• Macroscopic uncontrollable environment practically irreversible decoherence

Environment

Reversion: U U-1

• Microscopic or mesoscopic environment reversible decoherence

12.05.2005 12

Restricted Path Integrals (RPI)

• Continuous measurements presented by RPI

• Monitoring an observable decoherence

• Non-minimally disturbing monitoring dissipation

12.05.2005 14

Restricted Path Integral:

the paths, compatible

with the readout

Partial propagator: Utq'',q') =

=d[p]d[q] w[p,q] exp{(i/ћ) 0t (p dq - H dt)}

t

q

q’

q”

Weight functional

Evolution:tUt

t = Ut

0 (Ut

)†

Restricting Feynman path integral

12.05.2005 17

Effective Schroedinger equation

• Restricted Path Integral for monitoring A

Uta

(q'',q')=d[p]d[q] exp{(i/ћ)0t (p dq - H dt)

- 0t [A(t) - a(t)]2

dt}

• Effective Hamiltonian H[a] (p,q,t) = H(p,q,t) - i ћ (A(p,q,t) - a(t))2

• Effective Schroedinger equation

ta/t = [- (i/ћ) H - (A - a(t))2] t

a

Imaginary potential

12.05.2005 23

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

12.05.2005 24

Quantum informatics

• Qubits• Quantum computer • Quantum cryptography

• Quantum teleportation

12.05.2005 25

Qubits

• Two-level system

|0|1• Superposition

|0|1 quantum parallelism (entangled states)

(|0|1|00|01|10|11

(|0|1|x

12.05.2005 26

Quantum computer

• Quantum parallelism

(|0|1|x

• Calculation time tP(N) instead of t eN

• Quantum algorithms

• Factorization in prime numbers = finding the period of a periodic function (digital Fourier decomposition)

Cryptography

12.05.2005 27

Quantum cryptography

• Quantum cloning ||A |||A’ impossible

|1|A |1|1|A1, |2|A |2|2|A2Linearity: |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 |0and|1non-orthogonal• Distribution of code sequences

(factorization in prime numbers used)

12.05.2005 28

Quantum teleportation

• Correlation takes no time (pre-arranged)

• Communication with light speed

A B|A = |0|1 | B

| A

Meas

Qu correlation

(entanglement)

Meas Result i

Ui | B = |B

12.05.2005 30

Bell’s theorem

• EPR effect• Local realism • Bell’s inequality

• Aspect’s experiment

12.05.2005 31

EPR effect

• Maximal entanglement:

||||=|A+|A-|A-| A+ anticorrelation of spin projections Correlation of projections on different axes

S=0

S=1/2 S=1/2

12.05.2005 32

Local realism

• Anticorrelation: |A+|A-|A-| A+ • Assumtion of local realism means:

– If |A-, then really |A+– If | A+ , then really |A-

• Then measurement is interpreted as |Am1| Bn

2 |Am1| B-n 1(same particle)

12.05.2005 33

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-)

12.05.2005 34

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

12.05.2005 35

Conceptual problems

• Paradoxes: Schroedinger cat etc.• No reality previous to measurement• Linear evolution

c1|a10+c2|a20 c1|a1+c2|a2 reduction impossible

12.05.2005 36

Everett interpretation

• Linear evolution c1|a10+c2|a20 c1|a1+c2|a2

• Many classical realities (many worlds)• Selection = consciousness

12.05.2005 37

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)

12.05.2005 38

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.

12.05.2005 39

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)

12.05.2005 41

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)]

12.05.2005 42

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