Upload
christian-goodwin
View
220
Download
3
Tags:
Embed Size (px)
Citation preview
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