Transcript The Puzzling Story of the Neutral Kaon System or

Spooky action at distance
also for neutral kaons?
Testing Foundations in Quantum Mechanics
with the neutral K-meson system
by
Beatrix C. Hiesmayr
On leave: University of Vienna
&
Quantum Information Research Center
Bratislava
Physics 
 Particle Physics   Quantum Theory
Discrete 2010, Beatrix C. Hiesmayr
Outlook
Physics 
 Particle Physics   Quantum Theory
Part I: Bell inequalities in Particle Physics: What has
nonlocality to do with CP violation?
Part II: Heisenberg’s Uncertainty relation: A new
interpretation of measurements at accelerator facilities
Part II: How to detect the amount of entanglement?
Decoherence in HEP Experiments (KLOE detector)?
Part III: An advantage of entangled neutral kaons: offers
new possibilities for quantum erasure !!!
Discrete 2010, Beatrix C. Hiesmayr
About correlations…
drawn by R.A. Bertlmann to
the 60th birthday of J.S. Bell
Discrete 2010, Beatrix C. Hiesmayr
Outlook: DAPHNE, a F-factory (Italy)
"Physics with the KLOE-2
experiment at the upgraded
DAPHNE„
G. Amelino-Camelia, F. Archilli, D. Babusci, D. Badoni, G.
Bencivenni, J. Bernabeu, R.A. Bertlmann, D.R. Boito, C.
Bini, C. Bloise, V. Bocci, F. Bossi, P. Branchini, A. Budano,
S.A. Bulychjev, P. Campana, G. Capon, F. Ceradini, P.
Ciambrone, E. Czerwinski, H. Czyz, G.D’Ambrosio, E.
Dan´e, E. De Lucia, G. De Robertis, A. De Santis, P. De
Simone, G. De Zorzi, A. Di Domenico, C. Di Donato, B. Di
Micco, D. Domenici, S.I. Eidelman, O. Erriquez, R.
Escribano, R. Essig, G.V. Fedotovich, G. Felici, S.Fiore, P.
Franzini, P. Gauzzi, F. Giacosa, S. Giovannella, F. Gonnella,
E. Graziani, F. Happacher, B.C. Hiesmayr, B. H¨oistad, E.
Iarocci, S. Ivashyn, M. Jacewicz, F. Jegerlehner, T.
Johansson, J. Lee-Franzini, W. Kluge, V.V. Kulikov, A.
Kupsc, R. Lehnert, F. Loddo, P. Lukin, M.A. Martemianov,
M. Martini, M.A.Matsyuk, N.E. Mavromatos, F. Mescia, R.
Messi, S. Miscetti, G. Morello, D.Moricciani, P. Moskal, S.
Müller, F. Nguyen, E. Passemar, M. Passera, A. Passeri,
V. Patera, M.R. Pennington, J. Prades, L. Quintieri, A.
Ranieri, M. Reece, P. Santangelo, S. Sarkar, I. Sarra,
M.Schioppa, P.C. Schuster, B. Sciascia, A. Sciubba, M.
Silarski, C. Taccini, N. Toro, L. Tortora, G.Venanzoni, R.
Versaci, L.-T. Wang, W. Wislicki, M. Wolke, and J.
Zdebik
European Physics Journal C 68, Number 3-4,
619-681 (2010)
Discrete 2010, Beatrix C. Hiesmayr
The EPR scenario
Bell state:
 
1
2

1
2

1
2

1
2



1
2
1
2

0
H


l
 1
B0
l
l
l
 
r
 
l
 1 l 0
r
 V
l
K0
I
 
l
r
 K
 V
0
 K
0
 
0
... spin 1/2
r

... photon
 B
 II
0
 B0
l
l
 
r


 ... B-meson
... kaon
 K0
r
l
r
r

... qubit
 H
l
r
 B

r
r
r
... single neutron in
interferometer
R.A. Bertlmann, K. Durstberger, Y. Hasegawa and B.C. Hiesmayr PRA (2004)
 Filipp et al., PRL (2009)
Discrete 2010, Beatrix C. Hiesmayr
The EPR scenario
1935: Einstein-Podolsky-Rosen-PARADOX
The EPR reality criterion: “If without in
any way disturbing a system, one can
predict with certainty (i.e. with the
probability equal to one) the value of a
physical quantity, then there exists an
element of physical reality
corresponding to this physical
quantity.”
 Quantum Theory is not complete!
Discrete 2010, Beatrix C. Hiesmayr
What are Bell inequalities?
No spooky action
at distance!
realism
locality
free will
Local realistic theories:
Quantum Mechanics:
P (a , b)  P (a , c )  P (c , b)
inequalities for probabilities
 always satisfied!
quantum mechanical
probabilities may violate
the inequalities!
Experiment has to decide!
Discrete 2010, Beatrix C. Hiesmayr
Similarities/differences
Photons
  H l  V
r
V l H
Kaons
r

    K 0 l  K

0
 K
r
0
 K0 

r
l
0
0
P( H , n; H , m)  P(V , n;V , m)
P ( K , tl ; K , t r )  P ( K , tl ; K , t r )

 18 e S tl Ltr  e Ltl S tr
1
4
1  cos 2nm 
0
0

 2 cos( mt )  e  (tl tr )
No decay
S  L  0
0
0
P ( K , tl ; K , t r )  P ( K , tl ; K , t r )
0

1
4
0
1 cos(mt ) 

Discrete 2010, Beatrix C. Hiesmayr
Generalized Bell inequality for kaons
Bertlmann, Hiesmayr, PRA 63 (2001)
What can Alice & Bob measure?
measurement device
ta
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
Are you in a certain quasispin kn
or not at time ta?
kn 
1
 n  n
2
2

 n K 0  n K
0

quasispin
local realistic theories
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
• vary in times
• vary in quasi-spin
• or both
Discrete 2010, Beatrix C. Hiesmayr
Generalized Bell inequality for kaons
local realistic theories
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
I. Vary in time:
kn  km 
k n'  k m '  K
0
0
0
E ( K , ta ; K , tb )  cos m(ta  tb )  e ( ta  tb )
S Photon  2 2  2.8 Violation!
Kaons?
•Bertlmann, Bramon, Garbarino, Hiesmayr,
Phys. Lett. A (2004)
•Bertlmann, Hiesmayr, Phys. Rev. A (2001)
S Kaon ( t a , t b , t c , t d )  2 NO violation!
Strangeness oscillation/decay:
m
2m
x 

1

S
PROPOSITION:
The CHSH-inequality is violated iff x>2
for kaons or for other mesons x>2.6.
B-mesons: x=0.77
D-meson: x<0.03
Bs-mesons: x>20.6
Discrete 2010, Beatrix C. Hiesmayr
Bell-CHSH
forkaons
kaons
Bell-CHSHtype
type inequality
inequality for
Bertlmann, Hiesmayr, PRA 63 (2001)
0
0
0
0
SCHSH ( K , K , K , K ; t a , t b , t c , t d )
0
0
0
0
0
0
0
0
 E ( K , ta ; K , tb )  E ( K , ta ; K , tc )  E ( K , t d ; K , t b )  E ( K , t d ; K , t c )  2
Is it really not possible to distinguish
E ( K , t ; K , t )  cos m(t  t )  e
between local realistic theories and
quantum mechanics for neutral kaons in
Photons:
S
 2 2 a2.8direct
Violation! experiment?
0
0
a
 ( ta  tb )
b
a
b
Photon
Kaons?
S
Kaon
You have to be
•Bertlmann, Bramon, Garbarino, Hiesmayr,
( t a , t b , t c , t d )  2 NO violation!
Phys. Lett. A (2004)
more tricky!
•Bertlmann, Hiesmayr, Phys. Rev. A (2001)
Strangeness oscillation/decay:
x 
m
2m

1

S
PROPOSITION:
The CHSH-inequality is violated iff x>2
for kaons or for other mesons x>2.6.
B-mesons: x=0.77
D-meson: x<0.03
Bs-mesons: x>20.6
Discrete 2010, Beatrix C. Hiesmayr
!?Nonlocality related to a symmetry violation?!
Bell inequalities
CP violation
world
anti-world
Discrete 2010, Beatrix C. Hiesmayr
What has a symmetry violation to do with nonlocality?
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
II. Vary in quasi-spin:
kn  K S , km  K
k n'  k m '  K 1
0
 0
?! CP violation
related to nonlocality
!?
•Bertlmann, Grimus, Hiesmayr,PRA (2001)
•Hiesmayr, Found. of Phys. Lett (2001)
  0
 0
  0
Leptonic charge asymmetry:
( K L   l  l )  ( K L    l  l )

 (3.322  0.055) 10 3
 
 
( K L   l  l )  ( K L   l  l )
Discrete 2010, Beatrix C. Hiesmayr
Generalized Bell inequality for kaons
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
I. Vary in time:
kn  km 
k n'  k m '  K
0
0
0
E ( K , ta ; K , tb )  cos m(ta  tb )  e ( ta  tb )
S Photon  2 2  2.8 Violation!
Kaons?
S Kaon ( t a , t b , t c , t d )  2 NO violation!
Discrete 2010, Beatrix C. Hiesmayr
Decay is “kind of decoherence” ?
short-lived state
Kaon in time:
K (t ) 
0
1
2

e

S
2
t  im S t
KS  e
long-lived state

L
t  imL
2
t
KL

 state not normalized !!
Bertlmann, Grimus, Hiesmayr, Phys. Rev. A (2006)
!! particle decay is
System
``kind of decoherence´´ !!
 S  E (t  0)   S   E
Environment
 S  E ( t )  U ( t )  S  E ( 0)U † ( t )
S (t )  TrE S  E (t )   K i S  E (0) K i †
Discrete 2010, Beatrix C. Hiesmayr
Bell inequality sensitive to strangeness violated?
Hiesmayr, Eur. Phys. J. C (2007)
0
0
0
0
local realistic theories
SCHSH ( K , K , K , K ; t a , t b , t c , t d )
0
0
0
0
0
0
0
0
 E ( K , ta ; K , tb )  E ( K , ta ; K , tc )  E ( K , t d ; K , t b )  E ( K , t d ; K , t c )  2
Can we violate the BI for a certain initial
state and if, what is the maximum value?
Arbitrary initial state:
  r1e i K S K S  r2e i K S K L  r3e i K L K S  r4e i K L K L
1
Expectation value:
2
3
4
Discrete 2010, Beatrix C. Hiesmayr
Bell inequality sensitive to strangeness violated?
Can we violate the BI for a certain initial
state and if, what is the maximum value?
Hiesmayr, Eur. Phys. J. C (2007)
YES!!
The maximal violation is obtained for a
non-maximally entangled state
A. DiDomenico,Frascati
Smax  2.15
antisymmetric state
Frascati 2010, Beatrix C. Hiesmayr
How much nonlocality is in a decaying system ?
„dynamical“ nonlocality
2 2
Bell.
max
   
2.8
 n , n ;
m , m ; n , n ; m , m
tn tm t t T
n m
2.6
max
   
 n , n ;
Bell.
m , m ; n , n ; m , m
tn  t
m
T ; t tm 0
n
2.4
max
   
 n , n ;
Bell.
m , m ; n , n ; m , m
tn  t
m
0; t tm T
n
2.2
2
T [1010 s]
arbitrary,tn tm ' tn' tm t,Schrittweite P i 3
50
100
150
Discrete 2010, Beatrix C. Hiesmayr
Realizable Bell inequality for KLOE2 ?!?
Summary:
•
CP violation related to nonlocality
•
direct test not possible with
antisymmetric state (also not with
changed state due to regneration or due
to CPTV,…)
Bernabeu,
Mavromatos
Phys.Rev. D74 (2006) 045014
Open:
construct another BI which is sensitive to the
antisymmetric Bell state that is measured by
KLOE
Good:
have suitable framework
Discrete 2010, Beatrix C. Hiesmayr
Heisenberg‘s uncertainty relation
𝟏
∆𝑨 ∆𝑩 ≥
𝟐
∆𝑨 2 = 𝑨𝟐 - 𝑨 𝟐
𝑨, 𝑩 
…uncertainty of observable A,
standard deviations
Position and momentum:
𝟏
∆𝒙 ∆𝒑 ≥
𝟐
Your momentum is now known but where
have you been at that time of crime?
𝒉
𝒙, 𝒑  =
𝟐
Discrete 2010, Beatrix C. Hiesmayr
What questions are raised to the quantum system at accelerator
facilities?
Are you in a certain
quasispin kn or not at
at time ta?
measurement device
ta
kn,ta
kn 
1
 n  n
2
2

 n K 0  n K
0

quasispin
Expectationvalue(kn,ta)= Tr( O(kn) ta))
Effective formalism:
Expectationvalue(kn,ta)= Tr( Oeff(kn,ta) 
Heisenberg picture,
[Unpublished]
solves a lot of subtle problems
Discrete 2010, Beatrix C. Hiesmayr
Entropic quantum uncertainty principle
Heisenberg‘s uncertainty relation:
𝟏
∆𝑨 ∆𝑩 ≥
𝑨, 𝑩 
𝟐
Spectral decomposition:
A=
B=
…right hand side independent
𝒂|𝒂 𝒂|
𝒃|𝒃 𝒃|
of state and eigenvalues
𝟏
𝑯 𝑨 + 𝑯(𝑩) ≥ 𝟐 𝒍𝒐𝒈
𝒎𝒂𝒙𝒂,𝒃 | 𝒂 𝒃 |
𝑯 𝑿 = −𝒑 𝒍𝒐𝒈 𝒑 − 𝟏 − 𝒑 𝒍𝒐𝒈(𝟏 − 𝒑) …binary entropy
Example: 𝝈𝒙 , 𝝈𝒛 𝒎𝒂𝒙 =
𝟏
𝟐
, 𝑹𝑯𝑺: 𝟏
Discrete 2010, Beatrix C. Hiesmayr
Comparing measurements at different times may increase or
decrease the uncertainty in the system
𝑯 𝑶𝒆𝒇𝒇 (𝒌𝒏, 𝒕𝒏) + 𝑯(𝑶𝒆𝒇𝒇 (𝒌𝒎, 𝒕𝒎))
𝟏
≥ 𝟐 𝒍𝒐𝒈
𝒎𝒂𝒙𝒂,𝒃 | 𝒏 𝒎 |
blue… n=(kaon,t=0), m=(kaon,t)
red… n=(kaon,t=0), m=(long lived,t)
pink…n=(kaon,t=0), m=(short lived,t)
S  S / m
L  L / m
[t /  m ]
[Unpublished]
Discrete 2010, Beatrix C. Hiesmayr
How to test the entanglement?
Part II:
• a parameter z quantifying the amount of spontaneous
factorization of the wave function (Schrödinger-Furry
hypothesis)
• z can be measured by experimental data
(CERN,DAPHNE (Italy), KEK BELLE (Japan))
• connect z to a decoherence model (master equation)
with l quantifying the strength of the interaction with
the environment
• connection to measures of entanglement (Von Neumann
entropy, entanglement of formation or concurrence)
Discrete 2010, Beatrix C. Hiesmayr
Spontaneous factorization of the wave function
Schrödinger-Furry Hypothesis: (z  1)
|   |K

Sl
|K
L r
 |K
L l
|K
50%
50%
| K S   | K L
l
Sr
| K L  | K S 
r
l

Pz ( f1 , tl ; f 2 , tr )  1  2  2 (1  z ) Re *1 2
2
Observable:
QM
A
A
2
r

0
P( K , tl ; K , tr )  P( K 0 , tl ; K 0 , tr )  cos(mt )
(tl , tr ) 


cosh( 2 t )
0
with decoherence
(t )  A
without decoherence
CPLEAR-experiment (1998):
(t )(1  z )
16
z  0.1300..15
Bertlmann, Grimus and Hiesmayr,
Phys. Rev. D, 60, 114032 (1999)
Discrete 2010, Beatrix C. Hiesmayr
Spontaneous factorization of the wave function
Schrödinger-Furry Hypothesis (z  1) :
|   K

0
l
K
l
 K
r
50%
0
0 
|K  |K 
0
0
 K0
l
r
50%
0
|K   |K 0
l
r

Pz ( f1 , tl ; f 2 , tr )  1  2  2 (1  z ) Re *1 2
2
z
A
2
r

cos(mt )  12 z (cos(mt )  cos(m( t l  t r ))
0 (t l , t r ) 
0
cosh( 12 t )  12 z (cosh( 12 t )  cosh( 12 ( t l  t r ))
K ,K
CPLEAR-experiment (1998):
67
z K , K  0.4100..57
0
0
Bertlmann, Grimus and Hiesmayr,
Phys. Rev. D, 60, 114032 (1999)
Discrete 2010, Beatrix C. Hiesmayr
Testing entanglement/decoherence
decoherence in KS,KL/loss of
entanglement
zK
Bertlmann, Grimus,
Hiesmayr, Phys.Rev.
D (1999)
KLOE Coll.,
Phys. Lett. B (2006)
DiDomenico (2009)
S KL
decoherence in K0,K0:
0.16
 0.13 
0.15
z
0
z
KS K L
 0.018  0.040stat  0.07syst z
K0 K
z
KS K L
z
K0 K
 0.003  0.018stat  0.006syst
0
 0.4  0.7
 (0.10  0.21stat  0.04syst ) 105
 (1.4  9.5stat  3.8syst ) 107
But what about z(t)=1-e-lt?
B-mesons:
zB
H BL
Bertlmann, Grimus PRD (2001)
A.Go, BELLE, PRL (2008)
0
K0 K
zB
H BL
 0.06  0.1
 0.029  0.057
B.D. Yabsley (2008) arXiv:0810.1822 (D-mesons)
Discrete 2010, Beatrix C. Hiesmayr
“Erasing the past and impacting the future”
1801 Thomas Young:
Photons interfere!
Interference lost
because photon watched
(gain which way info)!
1982 Drühl & Scully:
Erasing the which
way info brings
interference back!
No wonder Einstein would be confused!
Discrete 2010, Beatrix C. Hiesmayr
The kaonic quantum eraser
Bramon, Garbarino, Hiesmayr, Phys. Rev. Lett. 92 (2004) 020405
Bramon, Garbarino, Hiesmayr, Phys. Rev. A 68 (2004) 062111
 many experiments with photons, neutrons or atoms
Why, kaons?
just another quantum system?
• because the working principle can be
Is this
demonstrated in A NEW
WAY,
all?
!!only!! possible with kaons
• and it can be performed at KLOE 2
Discrete 2010, Beatrix C. Hiesmayr
What does Particle Physics teach us about QM?
... a lot!!


Bell inequalities for qm system others than ordinary
•Hiesmayr, Found. of Phys. Lett. 14 (2001).
matter and light
•Bertlmann, Bramon, Garbarino, Hiesmayr, Phys. Lett. A 332, (2004) 355.
•Bertlmann, Grimus, Hiesmayr, Phys. Lett. A 289 (2001) 21.
•Bertlmann, Hiesmayr, Phys. Rev. A 63 (2001) 062112.
•....
How to measure entanglement or decoherence?
KEK (Japan) & DAFNE (Italy)
•Bertlmann, Durstberger, Hiesmayr, Phys. Rev. A 68 (2003) 012111.
•Bertlmann, Grimus, Hiesmayr,Phys. Rev. D 60 (1999) 114032.

“Kaonic” Quantum Erasers “Erasing the Past and
•Bramon, Garbarino, Hiesmayr, Phys. Rev. Lett. 92 (2004) 020405.
Impacting the Future”
•Bramon, Garbarino, Hiesmayr, Phys. Rev. A 68 (2004). 062111
Aharanov & Zubairy:
Science 307:875, 2005

Bohr’s Complementarity in two-path interferomety
or with CP violation (kaons are doubleslits given
freely by Nature)
Bramon,Garbarino, Hiesmayr, Phys. Rev. A 69 (2004) 022112.
Hiesmayr, Huber, Phys. Lett. A (2007)
Bramon, Garbarino, Hiesmayr, Eur. J. Phys. C 32 (2004) 377.
–
–
CPT tests, Lorentzsymmetry,…
Entanglement in a relativistic setting
Discrete 2010, Beatrix C. Hiesmayr
Thank you for Your attention!!!
University of Vienna
www.quantumparticlegroup.at
Double slit
Hansi Schimpf (Diploma)
Heidi Waldner (Diploma)
Theodor Adaktylos (Diploma)
Christoph Spengler (PhD)
Florian Hipp (Diploma)
Stefan Greindl (Diploma)
Markus Bauer (Diploma)
Andreas Gabriel (PhD)
David Schlögel (Diploma)
Marcus Huber (PostDoc)
Gerd Krizek (PhD)
B.C.Hiesmayr
Heidemarie Knobloch (Diploma)
Christina Peham (Diploma,without picture)
Paul Erker (without picture)
Sasa Radic (Diploma, without picture)
Sofia
2010,
Beatrix
C. Hiesmayr
Spooky
action
at distance
also
Take away messages
for neutral kaons?
• The full picture of entanglement and its manifestations is
still missing
• Investigating systems other than ordinary matter and
light adds new aspects (CP violation, dynamical nonlocality)
• …has/can be tested in experiments (loss of entanglement)
• In higher dimensions or for more particles new featues
arise (bounds on entanglement measures, simple inequalities
to detect and classify genuine entanglement)
… the story has just started
Sofia 2010, Beatrix C. Hiesmayr
A little history…
Drawn by R.A. Bertlmann to the
60th birthday of John Bell
CoQuS 2010, Beatrix C. Hiesmayr
Measurements: active & passive
Strangeness basis: K
0
0
K
0
“Active” measurement:
“Passive” measurement:
Semileptonic decay modes Q=S:
Strong interactions:
K0(sd)  (ud)+l++l
K0(sd)  (ud)+l-+l

0
K +p  L+
K0+n  K-+p, L+0
K0+p
K++n
Lifetime basis:
KKS+ K L
L+
K
K“Active” measurement:
L+0

2 Re 
1 
2
3
 3.2 10
“Passive” measurement:
Free propagation:
Sensitive to the decay modes:
any decay mode observed
before t+4.8 tS are identified
as KS at time t
Misidentification: few parts in 10-3!
Misidentification: few parts in 10-3!
2 ’s are identified as KS
3 ’s are identified as KL