Entanglement in Particle Physics

Reinhold A. Bertlmann Faculty of Physics, University of Vienna

Lecture at University of Siegen 11 July 2013

1 Contents

Ø Composite quantum systems, pure or mixed states nonlocal – contextual features, entanglement basis for quantum information, communication and computation

Ø Aim: to understand features of entanglement, quantum correlations phenomenological → conceptual → mathematical aspects

Ø Elementary particles – massive, internal symmetries, decay K-mesons strangeness B-mesons beauty Ø Bell inequalities for K-mesons BI for ﬂavour variation & relation to CP violation, BI for time variation

Ø Stability of quantum system understand decoherence – entanglement loss

Ø Outlook for future experiments

2 Part I

Entanglement and Bell inequalities

3 Schrödinger’s Cat

Superposition of quantum states: quantum particle can be in several diﬀerent states simultaneously !

Quantum entanglement: superposition of subsystems classically not possible !!

E. Schrödinger: “verschränkte Zustände … the whole is in a deﬁnite state, the parts individually taken are not.” 1935

Paradox: look into dead ? or alive ?

combination of 2 quantum systems → strange phenomenon: quantum information: Alice „knows“ about Bob without contact

not classically explainable → spooky

quantum state of 2 systems

Alice Bob spin measured by Alice and Bob 5 EPR Paradoxon

Einstein – Podolsky – Rosen 1935 Completeness of theory: Every element of physical reality must have counterpart in physical theory !

Physical reality: If we can predict with certainty a physical

quantity, without disturbing, then it is real !

↗ ↗

Alice Bob

if Alice then Bob will find or vice versa

EPR: QM incomplete ! EPR conclude spin at Bob is real reality not contained in QM however Bohr: QM complete ! 6 Bell‘s Theorem

Bell’s Theorem 1964

J.S. Bell: “ In a certain experimental situation all LRT (local realistic theories) are incompatible with quantum mechanics. “

Alice Bob

7 Bell Inequalities Expectation value for combined spin measurement E(a,b)

Inequality for different directions of measurement: S = | E(a,b) – E(a,b’) | + | E(a’,b’) + E(a’,b) | ≤ 2

CHSH-type In terms of probabilities P(a,b): E(a,b) = -1 + 4 P(a ⇑ , b ⇑)

P(a,b) ≤ P(a,c) + P(c,b) Wigner-type

Inequalities satisfied in each local realistic theory !

Comparison with quantum mechanics: _ EQM(a,b) = - cos(α-β) S QM = 2 √2 = 2.8 > 2

Experiment S Exp = 2.73 ± 0.02 Weihs, ... , Zeilinger 1998, Aspect etal. 1982, Fry etal. 1976, Clauser etal. 1972 Bell inequality violated in quantum mechanics and experiment !! 8 Tenerife Bell-Experiment

Transmission of entangled photons over 144 km in free space

Bell parameter: Zeilinger, Ursin, et al., 2009

Smax = 2.636 Sexp = 2.612 ± 0.114 9 Conclusion

10 Part II

Bell inequalities for strange mesons

11 Strange Mesons I

K – meson Kaon bound state of quark–antiquark (qq– ) u … up _ - d … down K0(ds) S=-1 K0(ds- ) S=+1 strangeness s … strange

quasi–spin

C … charge conjugation mass: 497 MeV JP = 0- pseudoscalar P … parity

strong interactions: S, CP conserving weak interactions: S, CP violating _ K0 ↔ K0 oscillation due to weak interactions |ΔS = 2|

12 Strange Mesons II Strange mesons selected by Nature to demonstrate fundamental principles of QM such as: 1) superposition

2) oscillation _ 3) decay property K0 K0 K0 quantum states π K0 -10 KS 10 sec π π K0 π -8 KL 10 sec π

4) regeneration

K0 = K + K 0 S _L K 0 0 KL = K + K K K K K S L S L absorbed in matter 13 Kaon Decays

14 Kaon Oscillation

15 Kaonic Qubits

16 Production of entangled Kaons

Matter – Antimatter collisions e+e- collider DA Φ NE in Frascati KLOE-2 experiment Di Domenico et al. - vector meson (ss): ϕ(1020) → KLKS 34%

Test of quantum coherence e+

_ K0 K0 detector Joint expectation value detector E(a.b) → E(ka,tl, kb,tr) Alice e- Bob ↑ ↑ dependent on - quasi-spin and time

production of Bell state at t = 0 17 Kaonic Bell Inequality of Wigner-type

Local Realistic Theories satisfy BI with choice: • ﬁx quasi-spin ⎯ vary time • vary quasi-spin ⎯ ﬁx time

Consider case: ﬁx time → vary quasi-spin of kaon → rotation in quasi-spin space _ 0 for BI we need 3 diﬀerent “angles” ⎯ quasi-spins: |KS〉, |K 〉, |K1〉

Bell inequality of Wigner-type F. Uchiyama 1997 _ _ 0 0 P(KS, K ) ≤ P(KS, K1) + P(K1, K ) P … probability

However, it contains unphysical CP-even state |K1〉 But ! BI inequality for physical CP parameter ⎯ experimentally testable !! How come ?

18 Experimental Inequality _ 0 0 |KS〉 = 1/N (p|K 〉 - q|K_ 〉) 0 0 BI optimal inequality for weights p, q of state |KS〉 |KL〉 = 1/N (p|K 〉 + q|K 〉)

p = 1 + ε, q = 1 – ε |p| ≤ |q| experimentally testable ! N2 = |p|2 + |q|2, |ε|≈10-3

Experiment: decay of K-mesons

Semileptonic decay of strange mesons:

Charge asymmetry

19 Charge Asymmetry

|p| ≤ |q| Bertlmann-Grimus-Hiesmayr 1999 Bell inequality for δ

δ ≤ 0 whereas:

BI experimentally violated ! _ consider 2 BI’s δ ≤ 0 and δ ≥ 0 when K0 → K0, p ↔ q CP conservation δ = 0 in contradiction to experiment !

Conclusion _ LRT are only compatible with strict CP conservation in K0K0 mixing ! _ δ ≠ 0 ⎯ K0K0 entanglement

CP violation nonlocal − contextual

20 BI for unitary Time Evolution

Next, consider case: ﬁx quasi-spin → vary time Joint expectation value

E(a.b) → E(ka,tl, kb,tr)

0 consider kaonic system: choose strangeness S = +1 ka = kb = K time evolution of states, respect unitary time evolution:

⎜ΩS,L(t)〉 state of all decay products

Joint expectation value in QM CP violation neglected

↑ ↑ Terms from decay products 21 Bell Inequality – general form

insert expectation value into BI

S = |EK0K0(tl, tr) – EK0K0(tl,tr’)| + |EK0K0(tl’,tr) + EK0K0(tl’,tr’)| ≤ 2

However: NO violation of BI for all possible times (tl,tr)

Reason: Ghirardi-Grassi-Weber 1991 interplay kaon decay strangeness oscillation

dependent on ratio x = Δm / Γ Δm = mL – mS , Γ … decay width

exper NO violation for 0 < x < 2 Experiment: x kaon = 0.95 similarly: B–mesons, D–mesons

Conclusion We cannot use time-variation of BI (CHSH type) to exclude LRT !

Question: Can we overcome this fact ? Yes ! 22 BI for decaying Systems

Bell inequality -2 ≤ S = |E(a,b) – E(a,b’)| + |E(a’,b) + E(a’,b’)| ≤ +2

converted into “witness” form B. Hiesmayr, A. Di Domenico etal. 2013

minall sep S[ρsep] ≤ S[ρ] ≤ maxall sep S[ρsep]

Expectation value ⎯ quantum mechanical correlations QM E (a,b) [ρ] = Tr (Oa ⊗ Ob ρ)

S – function of BI

QM S (a,a’;b,b’) = Tr { [Oa ⊗ (Ob – Ob’) + Oa’ ⊗ (Ob + Ob’)] ρ}

Oa … appropriate operators corresponding to decaying systems, e.g. kaons calculable inclusive CP violation

23 Experimental Test of BI

Intrinsic decay property also aﬀects separable states

Classical boundary for decaying system

⎜min/↑ maxall sep S [ρsep] ⎜ ≤ 2

2 for Γ → 0 stable systems leads to violation of Bell inequality !

We have got a tool to distinguish between LRT and QM ! experimental set-up production of Bell state ρ- = ⎢ψ- 〉〈 ψ-⎢ Example: Kaonic system 3 diﬀerent times corresponding to 3 Bell angles

ta = 0, tb = ta’ = 1,34 τS , tb’=2,80 τS

- minall sep S [ρsep] = - 0,58 S [ρ ] = - 0,69

- Experimentally feasible at DA NE Φ min S [ρsep] – S [ρ ] = 0,11 11 % with KLOE-2 detector 24 Part III

Decoherence of entangled beauty

25 Beauty Mesons

P - Neutral B – meson mB = 5.3 GeV J = 0 - _ - B0 (db), B0 (db) bound state of quark-antiquark +1 -1 b … beauty or bottom

QM formalism analogous to K – meson s → b _ B0 ↔ B0 oscillation

B decay: BH … heavy state BL … light state

0 0 Time evolution | BH (t) 〉, | BL(t) 〉 or | B (t) 〉, | B (t) 〉

according to Wigner-Weisskopf approximation

B – meson in contrast to K – meson -4 Δm = mH − mL = 3⋅10 eV large -1 -12 ΔΓ = ΓH − ΓL ≈ 0 small ΓB0 = τB0 = 1,5 ⋅10 sec

26 Production of B–Mesons e+e- collider at KEK, Tsukuba, Japan Asymmetric ring: e- 8.0 GeV e+ 3.5 GeV to study CP violation Kobayashi – Masukawa NP 2008 Quantum experiments Apollo Go et al. HEPHY, Richter, Vienna

B factory _ e+e- → ϒ(4S) → B0 B0 10.58 GeV

27 Creation of entangled B–Mesons

Resonance ϒ(4S) at 10.58_ GeV nearly at threshold of B0 B0 production

B factory

Creation of entangled state of B mesons

Quantum state ⎯ entangled beauty

Question: How to measure possible decoherence in entangled beauty ?

28 Decoherence Parameter

Test of quality of entanglement via decoherence option

Probability to detect beauty | b1 〉l on left side and beauty | b2 〉r on right side

Decoherence parameter ζ 0 ≤ ζ ≤ 1 Bertlmann-Grimus 1997

pure QM total decoherence, LRT 29 Asymmetry of Events Aim: to determine range of ζ by experimental data How ? consider as particles _ _ like-beauty events (B0, B0) and (_ B0, B_ 0) unlike-beauty events (B0, B0) and (B0, B0) Probabilities

Asymmetry directly sensitive to interference term

Aexper ζexper 30 Experimental Results

Decoherence parameter measures quantitatively Lorentz boost βγ = 0.425 deviations from pure QM Δz ≈ Δt⋅βγ c Problem: Exact vertex determination from tracks of decay products is diﬃcult task !

ζGo-Bay = 0.029 ± 0.057 BELLE ζRichter = − 0.045 ± 0.155 BELLE ζB-G = − 0.06 ± 0.10 ARGUS, CLEO _ Comparison with data from strangeness system K0K0

ζBGH = 0.13 ± 0.16 Bertlmann – Grimus – Hiesmayr, from CPLEAR data ζKLOE = 0.003 ± 0.018stat ± 0.006sys di Domenico etal, from CP suppressed decays Conclusion _ _ B0B0 and K0K0 systems are close to QM, ζ = 0, and far from total decoherence, ζ = 1, massive systems are entangled at macroscopic scale_ _ ⎯ LRT excluded 0.1 mm for B0B0 9 cm for K0K0 31 Decoherence – Open Quantum System

System S interacts with environment E → mixing of states decoherence S E Quantum master equation

density matrix of system

ρ = Σi pi | Ψi 〉〈Ψi | with 0≤pi ≤1

Dissipator ⎯ projectors to eigenstates of H

λ … decoherence parameter Bertlmann-Grimus 1998 eigenstates

start with entangled Bell state

32 Decoherence Parameter Relation

time dependence given by master equation Time dependent density matrix

↑ decoherence mixed state

Asymmetry of unlike–like events

↑ (1− ζ) in ζ – formalism

Parameter relation

33 Entanglement Loss – Decoherence

von Neumann entropy measures degree of uncertainty in quantum state

Entanglement of formation ⎯ measure for entanglement

0 ≤ E ≤ 1

Concurrence C

0 ≤ C ≤ 1

with binary entropy function Bertlmann-Durstberger-Hiesmayr 2003 Entanglement loss calculate concurrence -λt 1 − C ( ρ(t) ) = ζ (t) C ( ρ(t) ) = e 1 − E ( ρ(t) ) ≈ 1/ln2⋅ζ (t)

34 Part IV

Outlook

35 To do’s

Experimentalists in collaboration with theorists !

Ø Direct test of Bell inequalities, time variation ⎯ active measurements !

Ø Bell inequality with regenerator in kaon beam

KS , KL measurements, dependent on regeneration parameter Bramon-Escribano-Garbarino 2006 Hatice Tataroglu 2009

Ø Testing local realism in cascade decays ηc → VV → PP PP in τ – charm factory test of Clauser-Horne inequality in polarization correlation of entangled VV Li & Qiao 2009, proposal for BES-III at BEPC II in Beijing

Ø Test of local realism by CP violation of kaons Genovese 2005

36 To do’s

Ø High energy quantum teleportation with kaons incoming kaon collides with one kaon of an entangled pair Yu Shi 2006

utopic ??

Ø Environmental decoherence eﬀects ⎯ test of collapse models damping of oscillatory behaviour of mesons Bassi-Hiesmayr etal. 2013

Ø Entanglement in neutrino mixing and oscillation Blasone-Illuminati etal. 2008

Ø …………………….

37 The End