Transcript Classical World because of Quantum Physics

Institute for Experimental Physics
University of Vienna
Institute for Quantum Optics and Quantum Information
Austrian Academy of Sciences
Classical World because of
Quantum Physics
Johannes Kofler and Časlav Brukner
University of Leeds, United Kingdom
September 2006
Classical versus Quantum
Phase space
Hilbert space
Continuity
Events, ”Clicks”
Newton’s laws
Schrödinger + Projection
Local Realism
Violation of Local Realism
Macrorealism
Violation of Macrorealism
Determinism
Randomness
- Does this mean that the classical world is substantially different from
the quantum world?
- When and how do physical systems stop to behave quantumly and
begin to behave classically?
Macrorealism
[Leggett–Garg (1985)]
Macrorealism per se
Non-invasive measurability
“A macroscopic object, which has available
to it two or more macroscopically distinct
states, is at any given time in a definite one
of those states.”
“It is possible in principle to determine
which of these states the system is in
without any effect on the state itself or on
the subsequent system dynamics.”
Q(t1)
Q(t2)
t
t=0
t1
t2
Quantity: Q
t
t=0
t
Temporal correlations
t1
t2
t3
t4
All macrorealistic theories fulfill the
Leggett–Garg inequality
Violation  no objective properties prior to and
independent of measurements
When is Macrorealism violated?
Spin-1/2
Evolution
Observable
1/2
for
Violation of macrorealism
Classical Spin
precession around x
+1
Macrorealism
–1
classical
Violation of Macrorealism for macroscopically large spins?
Spin-j precession in magnetic field
(totally mixed state!)
j
Parity of eigenvalue m
of Jz measurement
classical limit
Violation of macrorealism for
arbitrarily large spins j
Shown for local realism
[Mermin, Peres]
The quantum-to-classical transition
Coherent spin state (t = 0):
exact measurement
fuzzy measurement
fuzzy measurement &
limit of large spins
This is (continuous and non-invasive) classical physics
of a rotated classical spin vector!
Transition to Classicality: General state
Quantum
General density matrix:
Classical
Probability to detect in a slot:

f can be negative!
Probability for result m:
h is non-negative!
Hamilton operator:
Hamilton function:
Classical limit:
Ensemble of classical spins with probability distribution h
Relation Quantum-Classical
inaccurate measurements
Quantum Physics
macroscopic objects
macroscopic objects
limit of large spins
Macro Quantum Physics
(no macrorealism)
?
Discrete Classical Physics
(macrorealism)
limit of large spins
Classical Physics
(macrorealism)
Is there a fundamental limit for
observability of quantum phenomena?
Algorithmic Complexity of Quantum States [Mora and Briegel]:
The length of the shortest string that encodes the preparation procedure for a
given state with a given precision ε.
Most of the states of N qubits are of complexity
2N random
amplitudes
Number of bits needed to realize the state:
Number of bits in the Universe [Lloyd]:
Limit [Davis]:

Every state is effectively a mixture over all pure states that are not
distinguishable within the precision ε
Conclusions
1.
2.
3.
Classical physics emerges from quantum laws
under the restriction of coarse-grained measurements,
not alone through the limit of large quantum numbers.
Conceptually different from decoherence. Not
dynamical, puts the stress on observability and works
also for fully isolated systems.
As the resources in the world are limited, there is a
fundamental limit for observability of quantum
phenomena (even if there is no such limit for the
validity of quantum theory itself).
quant-ph/0609079