Entanglement in Particle Physics

Transcription

1 Entanglement in Particle Physics Reinhold A. Bertlmann Faculty of Physics, University of Vienna Lecture at University of Siegen 11 July

2 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

3 Part I Entanglement and Bell inequalities 3

4 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 Paradox: look into dead? or alive? Schrödinger s cat superposition of 2 states: dead and alive cat entangled with decaying atom cat > = dead > g > + alive > e > 4

5 Entanglement 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

6 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 if Alice Bob then Bob will find EPR conclude spin at Bob is real reality not contained in QM or vice versa EPR: QM incomplete! however Bohr: QM complete! 6

7 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

8 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 In terms of probabilities P(a,b): E(a,b) = P(a, b ) P(a,b) P(a,c) + P(c,b) Wigner- type CHSH- type Inequalities satisfied in each local realistic theory! Comparison with quantum mechanics: Experiment E QM (a,b) = - cos(α-β) _ S QM = 2 2 = 2.8 > 2 S Exp = 2.73 ± 0.02 Weihs,..., Zeilinger 1998, Aspect etal. 1982, Fry etal. 1976, Clauser etal Bell inequality violated in quantum mechanics and experiment!! 8

9 Tenerife Bell- Experiment Transmission of entangled photons over 144 km in free space Bell parameter: S max = S exp = ± Zeilinger, Ursin, et al.,

10 Conclusion 10

11 Part II Bell inequalities for strange mesons 11

12 Strange Mesons I K meson Kaon bound state of quark antiquark (qq) _ - K 0 (ds) S=-1 K 0 (ds) - S=+1 strangeness u up d down s strange mass: 497 MeV J P = 0 - pseudoscalar quasi spin C charge conjugation P parity strong interactions: S, CP conserving weak interactions: S, CP violating _ K 0 K 0 oscillation due to weak interactions ΔS = 2 12

13 Strange Mesons II Strange mesons selected by Nature to demonstrate fundamental principles of QM such as: 1) superposition 2) oscillation 3) decay property π _ K 0 K 0 K 0 quantum states K 0 K S sec π π K 0 K L 10-8 sec π π 4) regeneration K 0 K S K L K S K L K 0 = K S + K_ L K L = K 0 + K 0 absorbed in matter 13

14 Kaon Decays 14

15 Kaon Oscillation 15

16 Kaonic Qubits 16

17 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) K L K S 34% Test of quantum coherence e detector Alice _ K 0 K 0 e - detector Bob Joint expectation value E(a.b) E(k a,t l, k b,t r ) dependent on quasi- spin and time production of Bell state at t = 0 17

18 Kaonic Bell Inequality of Wigner- type Consider case: Local Realistic Theories satisfy BI with choice: fix quasi- spin vary time vary quasi- spin fix time fix time vary quasi- spin of kaon rotation in quasi- spin space _ for BI we need 3 different angles quasi- spins: K S, K 0, K 1 Bell inequality of Wigner- type P(K S, K 0 ) P(K S, K 1 ) + P(K 1, K 0 ) F. Uchiyama 1997 P probability However, it contains unphysical CP- even state K 1 But! BI inequality for physical CP parameter experimentally testable!! How come? 18

19 BI Experimental Inequality optimal inequality for weights p, q of state K S p q experimentally testable! _ K S = 1/N (p K 0 - q K_ 0 ) K L = 1/N (p K 0 + q K 0 ) p = 1 + ε, q = 1 ε N 2 = p 2 + q 2, ε 10-3 Experiment: decay of K- mesons Semileptonic decay of strange mesons: Charge asymmetry 19

20 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 K 0 K 0, p q δ = 0 CP conservation in contradiction to experiment! Conclusion _ LRT are only compatible with strict CP conservation in K 0 K 0 mixing! δ 0 _ K 0 K 0 entanglement CP violation nonlocal contextual 20

21 BI for unitary Time Evolution Next, consider case: fix quasi- spin vary time Joint expectation value E(a.b) E(k a,t l, k b,t r ) consider kaonic system: choose strangeness S = +1 k a = k b = K 0 time evolution of states, respect unitary time evolution: Ω S,L (t) state of all decay products Joint expectation value in QM CP violation neglected Terms from decay products 21

22 Bell Inequality general form insert expectation value into BI S = E K 0 K 0(t l, t r ) E K 0 K 0(t l,t r ) + E K 0 K 0(t l,t r ) + E K 0 K 0(t l,t r ) 2 However: NO violation of BI for all possible times (t l,t r ) kaon decay Reason: interplay strangeness oscillation Ghirardi- Grassi- Weber 1991 dependent on ratio x = Δm / Γ Δm = m L m S, Γ decay width NO violation for 0 < x < 2 Experiment: x exper 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

23 Bell inequality BI for decaying Systems -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 min all sep S[ρ sep ] S[ρ] max all sep S[ρ sep ] Expectation value quantum mechanical correlations E QM (a,b) [ρ] = Tr (O a O b ρ) S function of BI S QM (a,a ;b,b ) = Tr { [O a (O b O b ) + O a (O b + O b )] ρ} O a appropriate operators corresponding to decaying systems, e.g. kaons calculable inclusive CP violation 23

24 Experimental Test of BI Intrinsic decay property also affects separable states Classical boundary for decaying system min/max all sep S [ρ sep ] 2 2 for Γ 0 stable systems leads to violation of Bell inequality! We have got a tool to distinguish between LRT and QM! production of Bell state ρ - = ψ - ψ - Example: Kaonic system 3 different times corresponding to 3 Bell angles t a = 0, t b = t a = 1,34 τ S, t b =2,80 τ S min all sep S [ρ sep ] = - 0,58 S [ρ - ] = - 0,69 experimental set- up min S [ρ sep ] S [ρ - ] = 0,11 11 % Experimentally feasible at DA Φ NE with KLOE-2 detector 24

25 Part III Decoherence of entangled beauty 25

26 Beauty Mesons Neutral B meson m B = 5.3 GeV J P = 0 - B 0 - _ (db), B 0 - (db) bound state of quark- antiquark +1-1 b beauty or bottom QM formalism analogous to K meson s b _ B 0 B 0 oscillation B decay: B H heavy state B L light state Time evolution B H (t), B L (t) or B 0 (t), B 0 (t) according to Wigner- Weisskopf approximation B meson in contrast to K meson Δm = m H m L = ev large ΔΓ = Γ H Γ L 0 small Γ B 0-1 = τ B 0 = 1, sec 26

27 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 B GeV 27

28 Creation of entangled B Mesons Resonance ϒ(4S) at _ GeV nearly at threshold of B 0 B 0 production B factory Creation of entangled state of B mesons Quantum state entangled beauty Question: How to measure possible decoherence in entangled beauty? 28

29 Decoherence Parameter Test of quality of entanglement via decoherence option Probability to detect beauty b 1 l on left side and beauty b 2 r on right side Decoherence parameter ζ 0 ζ 1 Bertlmann- Grimus 1997 pure QM total decoherence, LRT 29

30 Asymmetry of Events Aim: to determine range of ζ by experimental data How? consider as particles like- beauty events (B 0, B 0 )_ and (B 0,_ B 0 ) unlike- beauty events (B 0, B 0 ) and (B 0, B 0 ) Probabilities Asymmetry directly sensitive to interference term A exper ζ exper 30

31 Experimental Results Decoherence parameter measures quantitatively deviations from pure QM Problem: Exact vertex determination from tracks of decay products is difficult task! Lorentz boost βγ = Δz Δt βγ c ζ Go- Bay = ± BELLE ζ Richter = ± BELLE ζ B- G = 0.06 ± 0.10 ARGUS, CLEO _ Comparison with data from strangeness system K 0 K 0 ζ BGH = 0.13 ± 0.16 Bertlmann Grimus Hiesmayr, from CPLEAR data ζ KLOE = ± stat ± sys di Domenico etal, from CP suppressed decays Conclusion B 0 B 0 and K 0 K 0 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 B 0 B 0 9 cm for K 0 K 0 31

32 Decoherence Open Quantum System System S interacts with environment E mixing of states decoherence Quantum master equation S E density matrix of system ρ = Σ i p i Ψ i Ψ i with 0 p i 1 Dissipator projectors to eigenstates of H eigenstates λ decoherence parameter Bertlmann- Grimus 1998 start with entangled Bell state 32

33 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

34 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 calculate concurrence C ( ρ(t) ) = e - λt Bertlmann- Durstberger- Hiesmayr 2003 Entanglement loss 1 C ( ρ(t) ) = ζ (t) 1 E ( ρ(t) ) 1/ln2 ζ (t) 34

35 Part IV Outlook 35

36 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 K S, K L measurements, dependent on regeneration parameter Bramon- Escribano- Garbarino 2006 Hatice Tataroglu 2009 Ø Testing local realism in cascade decays η c 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

37 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 Ø Entanglement in neutrino mixing and oscillation Blasone- Illuminati etal Ø. 37

38 The End 38