EPR Pairs, Local Projection and Quantum Teleportation in Holography

Transcription

1 Strings and Fields 2016, YITP, Kyoto EPR Pairs, Local Projection and Quantum Teleportation in Holography Kento Watanabe (YITP, Kyoto) arxiv: [hep-th] (will appear in JHEP) with Tokiro Numasawa Noburo Shiba Tadashi Takayanagi (YITP -> KITP) (YITP -> Harvard U) (YITP)

2 Entanglement Measures & Related Phenomena motivated by Quantum Information theory EE, MI, Relative Entropy, Negativity, Complexity, Information metric Scrambling, Quantum Error Correction, Distillation Big Workshop!! Big Collaboration!! Hot topics in QFT & its Holographic Dual

3 Entanglement Measures & Related Phenomena motivated by Quantum Information theory EE, MI, Relative Entropy, Negativity, Complexity, Information metric Scrambling, Quantum Error Correction, Distillation Big Workshop!! Big Collaboration!! Hot topics in QFT & its Holographic Dual How about Operational Aspects? Quantum Operations Also important in many quantum process or protocols in QI However, so far, NOT investigated well in QFT & Holography.

4 Example : Quantum Teleportation in QM Task : sends [Bennet et al 93] s qubit to Protocol : Projection measurement on & Classically communication between Appropriate unitary operation to & Finally, can obtain the same qubit as s The protocol consists of LOCCs Local Operations & Classical Communications

5 Let s Try 3 Quantum Operations!!?? Focus on Partial Entangling Entangled Partial Swapping Swapped Partially prepare EPR pairs between two CFTs Vol (operated region) Partially exchange two CFTs (also EPR pairs) (# of EPR pairs crossing the edges) Local (Partial) Projection Projected to products Partially project out a CFT (Can) Reduce EE

6 Let s Try 3 Quantum Operations!!?? Focus on Partial Entangling Entangled Partial Swapping Swapped Partially prepare EPR pairs between two CFTs Vol (operated region) Partially exchange two CFTs (also EPR pairs) (# of EPR pairs crossing the edges) Local (Partial) Projection Partially project out a CFT Projected to products (Can) Reduce EE QFT Analog & Holographic Dual of Quantum Teleportation

7 Entangling & Swapping between two CFTs Path-Integral Pictures EEs after these operations

8 Path-Integral Pictures: Entangling Entangled Path-integral picture for density matrix: ( cf: replica method, TFD state ) Entangling

9 Entanglement Entropy after Entangling Non-contractive for solid torus Conformal Map Torus with period EE between two CFTs Dual BTZ BH Volume of the region we operated

10 Path-Integral Pictures: Swapping Swapped Path-integral picture for density matrix: ( cf: replica method, TFD state ) Swapping

11 Entanglement Entropy after Swapping Contractive for solid torus Conformal Map Torus Different cycle as Entangling EE between two CFTs # of EPR pairs crossing the edges

12 Local Projection Measurement in a CFT Local Projection as Boundary State Path-Integral Pictures EEs after the operation

13 Local Projection described by Boundary States Local (Partial) Projection No real space entanglement at each point in Factrization of n-pt function on Conformal Boundary states close each other No real space entanglement [Miyaji-Ryu-Takayanagi-Wen 14] Local Projection can be described by Boundary States [Rajabpour 15] More generally,

14 Path-Integral Pictures: Local Projection 1 interval jointed with 1-cut [Rajabpour 15] Its Dual Picture UHP with a twist operator Dual Minimal Geodesic : UV cut-off : Boundary entropy (ignore in this talk) AdS/BCFT : [ Takayanagi 11] [ Fujita-Tonii-Takayanagi 11] : Totally Geodesic Surface (ignore the tension in this talk)

15 2-cuts, 1-disjoint interval and Time-evolutions Annulus Half of Torus Dual Half of BTZ BH Identify Identify Cylinder

16 Example: EE in 2D Free Fermion CFT EE reduces by local projection at grows linearly in time (like quantum quench) After saturation, goes to zero (projection effect goes out)

17 Holographic EE after Projection or Entangling Disconnected Geodesics Connected Geodesic (Geodesic Length ) Entangling (Whole Torus) Only Connected Projection (Half of Torus) Connected or Disconnected BH Horizon Generated Reduced Connected Disconnected Disconnected Connected

18 Analogue of Quantum Teleportation in CFT & Holography Quantum Teleportation of Local Operator Partial Entangling + Local Projection + Local Unitary Transformation

19 Path-Integral Pictures: Quantum Teleportation Projection to Lorentzian Lorentzian Euclidean Euclidean Final state in Projection Entangling to Teleported!

20 Holographic Model of Quantum Teleportation Projection Projecting out 2-sided AdS BH Collapse Collapse of the holographic geometry ( The topology can change ) 1-sided AdS BH Effective Temperature reduces by half Teleportation to through the Euclidean BH cf. [Susskind 14, 16] Need more detail understandings. Traversable channel created by Swapping?? Classical Communication part??

21 Summary [hep-th] Partial Entangling Further Directions Higher dim. Generalizations 3 Quantum Operations Partial Swapping Vol( operated region ) (# of EPR pairs crossing the edges ) Torus Dual Time evolution BTZ BH More details on Quantum Teleportation in QFT & Holography Interpretation in Tensor Networks Torus?? Different Cycle as Entangling in CFTs & Holographic Duals Local (Partial) Projection CFT Analogue & Holographic Model of Quantum Teleportation of Local Operators New Entanglement Measures in QFT & Holography for Multi-partite Entanglement for Mixed States (Can) Reduce EE Dual Half of Torus Half of BTZ BH Time evolution But, Generate EE sometime (Growth like Quantum Quench) (Quantum Discord,?) from Local Operations etc (GHZ,?) THANKS!!

22 Appendix

23 Some Details on QFT Analogue of Quantum Teleportation The state after Entangling between and Act on the state with some conditions for the linearity Projecting the state by Projecting the state by Projecting the state by Final state in Teleported!

24 Time Evolution of Holographic EE after Entangling log t growth & decay Similar to locally excited state (local operator quench) in holographic CFTs No quasi-particle picture?? [Caputa-Nozaki-Takayanagi 14] [Asplund-Bernamonti-Galli-Hartman 14] Gravity dual : [Nozaki-Numasawa-Takayanagi 13]