arXiv:quant-ph/0602064v1 6 Feb 2006 Impossible colouring pseudo-telepathy game and non-local box Samir Kunkri 1 * , Guruprasad Kar 1† , Sibasish Ghosh 2 ‡ and Anirban Roy 3 § 1 Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India. 2 Department of Computer Science , The University of York, Heslington, York, YO10 5DD, United Kingdom. 3 International Center for theoretical Physics, Strada Costiera 11 34014, Trieste, Italy Abstract Here we will discuss a winning strategy of impossible colouring pseudo-telepathy game for the set of vectors having Kochen- Specker property in four dimension with single use of NL- box. Then we discuss some sufficient condition for the winning strategy of impossible colouring pseudo-telepathy game for general d-dimension with single use of NL-box. Introduction By performing measurement on an entangled quantum system two separate observer can obtain correlations that are nonlocal, in the sense that no local hidden variable (LHV) model can reproduce it. This was first proved by Bell in 1964 in terms of Bell inequality [1]. Later on Clauser, Horne, Shimony and Holt gave an experimental proposition of Bell’s inequality which is known as as CHSH inequality [2]. According to CHSH inequality all local hidden variable model must satisfy: |〈A 1 B 1 〉 + 〈A 1 B 2 〉 + 〈A 2 B 1 〉−〈A 2 B 2 〉| ≤ 2 where A 1 , A 2 are local spin measurement of a spin-half particle on Alice’s subsystem and B 1 , B 2 are measurement on Bob’s subsystem. But local measurement carried out on entangled quantum system can reach the value 2 √ 2. Cirelson’s showed [3] that this is the * E-mail:skunkri r@isical.ac.in † E-mail:gkar@isical.ac.in ‡ E-mail:sibasish@cs.york.ac.uk § E-mail:aroy@ictp.trieste.it 1