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Paper 1
Entanglement of approximate quantum strategies in XOR games
Dimiter Ostrev, Thomas Vidick
- Year
- 2016
- Journal
- arXiv preprint
- DOI
- arXiv:1609.01652
- arXiv
- 1609.01652
We show that for any $\varepsilon>0$ there is an XOR game $G=G(\varepsilon)$ with $Θ(\varepsilon^{-1/5})$ inputs for one player and $Θ(\varepsilon^{-2/5})$ inputs for the other player such that $Ω(\varepsilon^{-1/5})$ ebits are required for any strategy achieving bias that is at least a multiplicative factor $(1-\varepsilon)$ from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self-test for highly entangled states. Up to the exponent $-1/5$ the scaling of our bound with $\varepsilon$ is tight: for any XOR game there is an $\varepsilon$-optimal strategy using $\lceil \varepsilon^{-1} \rceil$ ebits, irrespective of the number of questions in the game.
Open paperPaper 2
Knowledge-Concealing Evidencing of Knowledge about a Quantum State
Emily Adlam, Adrian Kent
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1706.06963
- arXiv
- 1706.06963
Bob has a black box that emits a single pure state qudit which is, from his perspective, uniformly distributed. Alice wishes to give Bob evidence that she has knowledge about the emitted state while giving him little or no information about it. We show that zero-knowledge evidencing of such knowledge is impossible in quantum relativistic protocols, extending a previous result of Horodecki et al.. We also show that no such protocol can be both sound and complete. We present a new quantum relativistic protocol which we conjecture to be close to optimal in security against Alice and which reveals little knowledge to Bob, for large dimension $d$. We analyse its security against general attacks by Bob and restricted attacks by Alice.
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