Correlation/Communication complexity of generating bipartite states

We study the correlation complexity (or equivalently, the communication complexity) of generating a bipartite quantum state ρ. When ρ is a pure state, we completely characterize the complexity for approximately generating ρ by a corresponding approximate rank, closing a gap left in Ambainis, Schulman, Ta-Shma, Vazirani and Wigderson (SIAM Journal on Computing, 32(6):1570-1585, 2003). When ρ is a classical distribution P (x, y), we tightly characterize the complexity of generating P by the psd-rank, a measure recently proposed by Fiorini, Massar, Pokutta, Tiwary and de Wolf (STOC 2012). We also present a characterization of the complexity of generating a general quantum state ρ. Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542. Email: [email protected] Department of Electrical Engineering and Computer Science, 2260 Hayward Street, University of Michigan, Ann Arbor, Michigan, 48109-2121, USA. Email: [email protected] Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542. Email: [email protected] Department of Computer Science and Engineering and The Institute of Theoretical Computer Science and Communications, The Chinese University of Hong Kong. Email: [email protected]