1 / 16

Entanglement sampling and applications

This work explores the interplay between entanglement and uncertainty relations in quantum games, particularly focusing on scenarios involving an adversary (Eve) and a quantum state (Alice). Collaboratively authored by Omar Fawzi, Frédéric Dupuis, and Stephanie Wehner, the research demonstrates that at least half of the quantum memory is necessary for maximizing guessing probability (Pguess). The findings have implications for two-party cryptography and secure computation, highlighting the significance of entanglement and new uncertainty relations to enhance security in quantum communications.

ciara-white
Download Presentation

Entanglement sampling and applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Entanglement sampling and applications Process Omar Fawzi (ETH Zürich) Joint work with FrédéricDupuis (Aarhus University) and Stephanie Wehner (CQT, Singapore) arXiv:1305.1316

  2. Uncertainty relation game Eve Alice Choose n-qubit state Choose random EVE … Choose n-qubit state X1 Xn X2 Xn-1 Choose random Guess X Maximum ? … X1 Xn X2 Xn-1 Guess X Maximum Pguess?

  3. Uncertainty relation game • Can Eve do better with different ? • No [Damgard, Fehr, Salvail, Shaffner, Renner, 2008] Measure in X Guess X Between 0and n Notation:

  4. Uncertainty relations with quantum Eve Eve has a quantum memory A Measure in E X Guess X using E and Maximum ? [Berta, Christandl, Colbeck, Renes, Renner, 2010]

  5. Uncertainty relations with quantum Eve Measure in A X E Measure in X

  6. Uncertainty relations with quantum Eve E.g., if storage of Eve is bounded? Uncertainty relation + chain rule  using maximal entanglement Converse Is maximal entanglement necessary for large Pguess? Main result: YES At least n/2 qubits of memory necessary

  7. The uncertainty relation E=X between –n and n Max entangled Max entangled • Measure for closeness to maximal entanglement • Log of guessing prob. between 0 and n

  8. The uncertainty relation Max entanglement

  9. General statement X C More generally: Gives bounds on Q Rand Access Codes Meas in Θ M A A Example: E E

  10. Applicationtotwo-party cryptography ?? ?? “I’m Alice!” password Stored password Equal? Malicious ATM: tries to learn passwords Yes/No Malicious user: tries to learn other customers passwords

  11. Application to secure two-party computation • Unconditional security impossible [Mayers 1996; Lo, Chau, 1996] • Physical assumption: bounded/noisy quantumstorage [Damgard, Fehr, Salvail, Schaffner 2005; Wehner, Schaffner, Terhal 2008] • Security if Using new uncertainty relation • Security if n: number of communicated qubits

  12. Proof of uncertainty relation Step 1: X Conditional state Meas in Θ A E

  13. Proof of uncertainty relation Step 2: Write by expanding in Pauli basis

  14. Proof of uncertainty relation Relate and Observation 1: Not good enough

  15. Proof of uncertainty relation Relate and Observation 1: Observation 2: Combine 1 and 2  done!

  16. Conclusion • Summary • Uncertainty relation with quantum adversary for BB84 measurements • Generic tool to lower bound output entropy using input entropy • Open question • Combine with other methods to improve? ?

More Related