Controlled Hawking Process by Quantum Information

1. ブラックホールと量子エネルギーテレポーテーションブラックホールと量子エネルギーテレポーテーション 改め Controlled Hawking Process by Quantum Information Masahiro Hotta Tohoku University arXiv:0907.1378

2. Black Hole Entropy Problem In classical theory, black holes are considered to absorb matter, but emit nothing. By virtue of the no-hair theorem, a black holes was regarded as a candidate of the final state of matter. However, in 1974, S. Hawking argued that black holes emit thermal radiation by taking account of quantum effect of fields. This essentially establishes the belief that black holes are thermo-dynamical existence, which have entropy proportional to event horizon area. gravitational constant thermal radiation Usually thermo-dynamical systems have statistical dynamical description using entropy concept. However, the statistical dynamical picture of black holes has not been established yet. This is called the black hole entropy problem.

3. In this presentation, we shed light on the problem by using a gedanken experiment of quantum energy teleportation (QET). The argument does not require un-established physics of quantum gravity. By using only semi-classical analysis, we can make significant statementsabout memory of black holes. In classical description of black holes, after the outside spacetimes are stabilized, they forget any memories except mass, charge and angular momentum (no-hair theorem). However, we can show that even after the outside spacetime become static,black holes still remember in a quantum mechanical waywhat they swallowed. Thermal relaxation process of black holes is also suggested, which time scale is of order of the inverse of black hole temperature.

4. The QET protocols attain energytransfer by Local Operations and Classical Communication (LOCC) without breaking causality and local energy conservation.

5. Let us consider two empty boxes placed separately. Nothing! Nothing!

6. Let us infuse energy to one of the boxes. energy

7. Something happens inside the box and outputs a numerical number 0 or 1 to be announced to the other box. energy Abracadabra 0 ! (or 1! ) Nothing! Nothing!

8. In the other box, some operation is performed dependent on the announced abracadabra (0 or 1). After that, energy can be extracted from the box which was empty at the beginning. teleported energy! energy Abracadabra 0 ! (or 1! ) Scientific magic tricks can achieve this amazing magic !!

9. POINT: WHAT is “NOTHING” in Quantum Physics ? 無 “Nothing”

10. POINT: WHAT is “NOTHING” in Quantum Physics ? GROUND STATE (Quantum Fluctuation) NOTHING in Quantum Physics =GROUND STATE with Quantum Fluctuation entanglement

11. QET protocols can be considered in a lot of quantum systems including ○Spin Chains ○ Trapped Ions ○Massless Quantum Fields ○Quantum Hall Edge Currents ○1 Dim. BEC (Trapped Atoms) ○Carbon Nano Tubes ○SQUID Chains ： ←Today’s talk Today, let us focus on the protocol for quantum fields in near-horizon regions of black holes.

12. Let us grasp a general idea of this QET mechanism ! M.Hotta, J. Phys. Soc. Jp. 78, (2009) 034001 M.Hotta, Phys.Lett.A372(2008)5671 M.Hotta, Phys.Rev.D78(2008)045006

13. Amplitude of fluctuation Quantum Fluctuation in the Ground State of Many-Body System Alice Bob spin chain The ground state has many components of quantum fluctuation as superposition of states. In the above figure, red and blue lines simply describe those different components.

14. Amplitude of fluctuation Amount of energy increases on average ! If an unitary operation independent of Alice’s measurement result acts on Bob’s qubit, the blue-lined component may become suppressed, but the red-lined component becomes large. Thus, on average, positive amount of energy must be infused in the fluctuation.

15. Amplitude of fluctuation Quantum Fluctuation in the Ground State Alice Bob entanglement In QET case, we use the ground-state entanglement between fluctuation around Alice and fluctuation around Bob .

16. Amplitude of fluctuation Measurement by A Information around B via entanglement Alice’s measurement specifies the value of α and its corresponding fluctuation component. In the figure, the blue-lined component is selected and the red-lined component vanishes . Because of the entanglement, Alice’s measurement result α includes information about fluctuation around Bob.

17. Amplitude of fluctuation Local Unitary Operation by B By getting information about α from Alice, Bob knows how the fluctuation in front of Bob behaves. Bob can choose an appropriate unitary operation in order to suppress the fluctuation.

18. Amplitude of fluctuation Local Operation of Bob dependent of measurement results B Extraction of Energy from Spin Chain A By squeezing the fluctuation locally, Bob can obtain energy from the spin chain. The extracted energy was hidden in Bob’s region from the start ! Thus no energy carrier is hired in the QET protocol !!

19. Impact to Black Hole Entropy Problem ? QET in BH spacetime = Controlled Hawking Process by Measurement Information B 1bit Measurement information A

21. negative energy flux unitary operation and energy extraction t=T positive energy flux b=0 or 1 Horizon measurement and energy injection t=0 Controlled Hawking Process by Measurement Information

22. If B does not perform the operation, …. positive energy flux

23. If B performs the operation, the horizon recedes ! The black-hole entropy decreases ! negative energy flux positive energy flux

24. （１） For N fields, A performs the measurement. measurement results The result-dependent wave packets are absorbed by the black hole. The amount of energy of the wave packets does not depends on the measurement result. Horizon

25. （２） B performs result-dependent operations for N fields. absorbed information about the measurement result The wave packets with negative energy are absorbed by the black hole and recede the horizon. extracted energy Shifted Horizon

26. If B uses incorrect information for the operations, the amount of energy extracted by QET decreases. Horizon

27. Brief Summary The amount of energy infused by the first measurement is independent of the measurement result. Thus, the outside spacetimes of black holes are also independent of the result from the classical theoretical point of view. This implies that the classical black holes do no remember the detailed information of falling matters. However, the black holes still remember what they swallowed in a quantum mechanical way. Via the QET protocol, we can extract energy from the black holes by using correct measurement results. If the operations is based on incorrect information of the measurement result, the amount of extracted energy decreases. Note that the amount of energy decreases in time. This describes thermal relaxation of the black holes. The time scale of the relaxation is of order of inverse of the black hole temperature, as naturally expected.

28. In the later, let me explain details by use of equations !

29. In order to discuss classical behaviors of horizon shift of black holes explicitly, let us adopt a two-dimensional solvable model, CGHS model, for simplicity. The obtained results are essentially the same as those of spherically symmetric black holes of Einstein gravity in higher dimensions.

30. Classical CGHS MODEL Black Hole solution Event Horizon

31. Using the light-cone coordinates, Because the horizons stay at , the black hole geometries can be described by the flat metric in near-horizon regions.

32. Quantum fields in the classical black-hole spacetime can be analytically solved. Falling-Matter Mode Out-Going Mode Exact Solution with Falling Matter

33. large-black-hole and near-horizon limit Even if the incoming energy flux exists, the geometry is described by the flat metric near the horizon in these coordinates.

34. It is possible to observe horizon-shift explicitly using rescaled coordinates such that Solution in the New Coordinates:

35. The outside spacetime becomes static soon after the matter is absorbed ! Horizon-Shift

36. energy density Hamiltonian vacuum state Horizon

37. Quantum Energy Teleportation in Black-Hole Spacetime The thermal equilibrium states of quantum fields in the black-hole spacetime are described by the entangled Hartle-Hawking state. Near the horizon, this state is reduced into the Minkowski vacuum state in the large-mass limit. Let us consider a QET protocol in the near-horizon region in order to investigate quantum properties of black holes.

38. In the near-horizon region, we get 1-bit information about quantum fluctuation of a field by interacting with a two-level spin and measuring the spin. This indirect measument is described by the following measurement operators: NOTE:

39. Post-Measurement States of Quantum Fields: The amount of energy for the state is independent of the measurement result and given by This energy is infused by the measurement device. The wave packets with this energy fall into the black hole and increase the mass and entropy of the black hole. Because the amount of energy is independent of the measurement result, the outside spacetime is the same, independent of the result.

40. Horizon

41. Classical treatment of spacetime is valid for the large N limit. Horizon

42. After time T passes, perform an operation dependent on the measurement result for the quantum fluctuation. real parameter fixed later Post-Measurement State

43. Average Energy after the Operation

44. By setting This implies that positive energy is transferred from the quantum fluctuation to the outside. Simultaneously, wave packets with negative energy are generated during the operation and fall into the black hole. This decreases the mass and entropy of the black hole.

45. Horizon

46. extracted energy Horizon

47. If wrong information about the measurement result is adopted, the operation does not extract but gives energy to the flctuation. When the errors happen for ¼ of N fields, the amount of energy extracted from the black hole becomes zero on average.

48. Horizon

49. Come back to Summary The amount of energy infused by the first measurement is independent of the measurement result. Thus, the outside spacetimes of black holes are also independent of the result from the classical theoretical point of view. This implies that the classical black holes do no remember the detailed information of falling matters. However, the black holes remember what they swallow in a quantum mechanical way. Via the QET protocol, we can extract energy from the black holes by using correct measurement results. If the operations is based on incorrect information of the measurement result, the amount of extracted energy decreases. Note that the amount of energy decreases in time. This describes thermal relaxation of the black holes. The time scale of the relaxation is of order of inverse of the black hole temperature, as naturally expected.