The superiority of quantum computers over classical ones disappears when the quantum system is subjected to noise. At sufficiently high noise levels, the classical computer can efficiently simulate the noisy quantum statistics. One way of defining this noise threshold is presented in [1] as the amount required such that all two-qubit gates in the computer can never entangle a separable input; an efficient algorithm is presented which samples the quantum probabilities. If the design of the computation permits only a restricted set of quantum measurements, the space of states yielding positive probabilities under these measurements (the dual cone) is larger than quantum state space. One may define a new notion of separability in these state spaces [2] and use this to calculate (different) noise levels at which bipartite gates cannot produce entanglement with respect to this new state space. By adapting the algorithm of [1], it has been shown [3,4] that these noise levels can be tighter than the quantum ones, thus narrowing down the region of “useful” quantum computation. In this talk, we discuss separability conditions for some non-quantum state spaces by employing steering.
[1] A. Harrow and M. Nielsen, Phys. Rev. A 68, 012308 (2003)
[2] H. Barnum, E. Knill, G. Ortiz, and L. Viola, Phys. Rev. A, 68, 032308 (2003)
[3] N. Ratanje and S. Virmani, Phys. Rev. A 83, 032309 (2011)
[4] N. Ratanje and S. Virmani, arXiv:quant-ph/1201.0613