Interpolating Between Quantum Teleportation Protocols MICHA STUDZISKI UNIVERSITY
Interpolating Between Quantum Teleportation Protocols MICHAŁ STUDZIŃSKI, UNIVERSITY OF GDAŃSK JOINT WORK WITH: M. HORODECKI (UNIVERSITY OF GDAŃSK) M. M. WILDE (LOUISIANA STATE UNIVERSITY) 17. 06. 2019, 51 th Symposium on Mathematical Physics, Toruń
Outline of the talk: • Various Types of Quantum Teleportation Protocols • Convex Split Lemma • Unified Teleportation Scheme • Interpolating Between Teleportation Schemes • Multipartite Quantum Teleportation Schemes • Entanglement Fidelity of the Protocols
QUANTUM TELEPORTATION PROTOCOLS
Standard Quatum Teleportation (Bennet et al. PRL 70(13): 1895 -1899, 1993)
Port-based Teleportation For d=2; PRL 101(24): 240501, 2008 For d>2; Sci. Rep. (2017); 7: 10871 & NJP 20. 5 (2018): 053006
Two Types of PBT Scheme Deterministic PBT Probabilistic PBT M. Christandl, F. Leditzky, Ch. Majenz, G. Smith, F. Speelman, M. Walter, ar. Xiv: 1809. 10751 v 1
Why do we care? Identification of cause-effect relations Instantenous nonlocal quantum computations Quantum channels discrimination Some aspect of commuication complexity Port-based Teleportation Universal programmable quantum processor Cryptographic attacks
QUANTUM TELEPORTATION PROTOCOLS • Is there any unified scheme? • Can we produce new quantum teleportation protocols? Our list of wishes: Ø To reduce amount of entaglement Ø To teleport more particles with higher fidelity Ø To use simpler measurements Ø Possibly new applications
General Idea Behind the Quantum Teleportation ALICE BOB Resource State
CONVEX-SPLIT LEMMA A. Anshu, V. K. Devabathini, R. Jain, PRL 119, 120506 (2017)
Convex-split Lemma •
Convex-split Lemma •
THE GENERALISED TELEPORTATION PROTOCOL
The generalised teleportation protocol •
The generalised teleportation protocol •
What about the efficiency? •
What about the efficiency? •
INTERPOLATING BETWEEN TELEPORTATION SCHMES
EXAMPLES •
EXAMPLES •
GENERALISATIONS TO NEW PROTOCOLS •
FURTHER DEVELOPMENTS •
REFERENCES Port-based Teleportation • S. Ishizaka, T. Hiroshima, PRL 101, 240501 (2008) - solution for qubits • S. Ishizaka, T. Hiroshima, PRA 79, 042306 (2009) – solution for qubita + optimality • M. Studziński et al. Sci. Rep. 7, 10871 (2017)- solution for higher dimensions + optimality • M. Mozrzymas et al. NJP 20. 5, 053006 (2018)- solutions for higher dimensions + optimality • M. Christandl et al. ar. Xiv. 1809. 10751 -full description of asymptotic performance Applications of Port-based Teleportation • S. Beigi, R. Koenig, NJP 13, 093036 (2011) - position based quantum cryptography • H. Buhrman et al. PNAS 113, 3191 -3196 (2016) – Bell inequality violations vs complexity theory • G. Chiribella, D. Ebler, Nature Communication 10, 1472 (2018) – identification of cause-effect relations • S. Pirandola et al. NPJ Quantum Information 5, 3 (2019) – limitations on quantum channels discrimination
- Slides: 23
