Strings and Fields 2016, 2016/08/10 @ YITP, Kyoto EPR Pairs, Lo Local Projection and Quantum Tele leportation in Holography in Kento Watanabe (YITP, Kyoto) arXiv: 1604.01772 [hep-th] with Tokiro Numasawa (YITP -> KITP) Noburo Shiba (YITP -> Harvard U) (will appear in JHEP) Tadashi Takayanagi (YITP)
Entanglement Measures & Related Phenomena motivated by Quantum Information theory EE, MI, Relative Entropy, Negativity, Complexity, Information metric Big Workshop !! Scrambling, Quantum Error Correction, Distillation … Big Collaboration !! Hot topics in QFT & its Holographic Dual
Entanglement Measures & Related Phenomena motivated by Quantum Information theory EE, MI, Relative Entropy, Negativity, Complexity, Information metric Big Workshop !! Scrambling, Quantum Error Correction, Distillation … Big Collaboration !! Hot topics in QFT & its Holographic Dual How about Operational Aspects ? Quantum Operations quantum process Also important in many in QI or protocols However, so far, NOT investigated well in QFT & Holography ….
Example : : Quantum Tele leportation in in QM [Bennet et al ‘93] Task : sends ’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
Let’s Try 3 Quantum Operations !! Focus on ?? Partial Entangling Partial Swapping Entangled Swapped Partially exchange two CFTs (also EPR pairs) Partially prepare EPR pairs between two CFTs (# of EPR pairs crossing the edges) Vol (operated region) Local (Partial) Projection Projected to products (Can) Reduce EE Partially project out a CFT
Let’s Try 3 Quantum Operations !! Focus on ?? Partial Entangling Partial Swapping Entangled Swapped Partially exchange two CFTs (also EPR pairs) Partially prepare EPR pairs between two CFTs (# of EPR pairs crossing the edges) Vol (operated region) Local (Partial) Projection Projected QFT Analog & Holographic Dual of to products “Quantum Teleportation” (Can) Reduce EE Partially project out a CFT
Entangling & & S Swapping between tw two CFT FTs Path-Integral Pictures EEs after these operations
Path th-Integral Pict ictures: En Entangli ling Entangled Path-integral picture for density matrix: ( cf: replica method, TFD state ) Entangling
En Entangle lement En Entr tropy aft fter En Entangli ling Non-contractive for solid torus Conformal Map Torus with period Dual BTZ BH EE between two CFTs Volume of the region we operated
Path th-Integral Pict ictures: Swappin ing Swapped Path-integral picture for density matrix: ( cf: replica method, TFD state ) Swapping
Entan anglement Entr tropy aft fter er Swap apping Contractive for solid torus Conformal Map Torus Different cycle as Entangling EE between two CFTs # of EPR pairs crossing the edges
Lo Local Projection Measurement in in a CFT FT Local Projection as Boundary State Path-Integral Pictures EEs after the operation
Lo Local l Projection desc scribed by y Bou oundary ry 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] More generally, [Rajabpour‘15] Local Projection can be described by Boundary States
Path th-Integral Pict ictures: Loc ocal Proje ojectio ion 1 interval jointed with 1-cut [Rajabpour‘15] : UV cut-off : Boundary entropy UHP with a twist operator (ignore in this talk) Dual Its Dual Picture AdS/BCFT : Minimal Geodesic [ Takayanagi’11] [ Fujita-Tonii- Takayanagi’11] : Totally Geodesic Surface (ignore the tension in this talk)
2-cu cuts, 1-dis isjo joint in inter erval al an and Tim Time-evolutions Annulus Half of Torus Cylinder Dual Identify Half of BTZ BH Identify
Ex Exam ample le: EE EE in in 2D Fr Free ee Fer ermio ion CFT FT After saturation, EE reduces by local projection at grows linearly in time goes to zero (like quantum quench) (projection effect goes out)
Holo olographic EE EE aft fter Proje ojectio ion or or En Entangli ling Disconnected Connected Geodesic Geodesics (Geodesic Length ) Connected Only Entangling Projection or Connected Disconnected (Whole Torus) (Half of Torus) BH Horizon Connected Connected Generated Reduced Disconnected Disconnected
Analogue of Quantum Teleportation in CFT & Holography “Quantum Teleportation” of Local Operator Partial Entangling + Local Projection + Local Unitary Transformation
Path th-Integral Pict ictures: Qua uantum Tele eleportatio ion Projection Lorentzian Lorentzian to Euclidean Euclidean Final state in Entangling Projection to Teleported !
Hol olographic Mod odel of of Quantum Tele leportation Projecting out Collapse of the holographic geometry ( The topology can change ) Projection 2-sided AdS BH 1-sided AdS BH Effective Temperature reduces by half Collapse Teleportation to through the Euclidean BH cf. [Susskind ‘14, ‘16] Traversable channel created by Swapping ?? Need more detail understandings …. “Classical Communication” part ??
Summary 3 Quantum Operations in CFTs & Holographic Duals 1604.01772 [hep-th] ?? Partial Entangling Local (Partial) Projection Partial Swapping (Can) Reduce EE Dual Half of Torus Half of BTZ BH Vol( operated region ) (# of EPR pairs crossing the edges ) Time evolution Dual Different Cycle as Torus Torus BTZ BH But, Generate EE sometime Entangling (Growth like Quantum Quench) Time evolution CFT Analogue & Holographic Model of “Quantum Teleportation” of Local Operators Further Directions … New Entanglement Measures in QFT & Holography Higher dim. Generalizations (GHZ, …?) for Multi-partite Entanglement More details on “Quantum Teleportation” in QFT & Holography (Quantum Discord,…?) for Mixed States … Interpretation in Tensor Networks from Local Operations … etc THANKS !!
Appendix
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 !
Tim Time Evol olutio ion of of Holo olographic EE EE aft fter En Entangli ling 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]
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