We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identificationâ€¦ (More)

We study the entanglement cost under quantum operations preserving the positivity of the partial transpose (PPT operations). We demonstrate that this cost is directly related to the logarithmicâ€¦ (More)

Partitions can be graphically represented by Young frames , which are Young tableaux with empty boxes. The i-th part Î»i corresponds to thei-th row of the frame, consisting of Î»i boxes. Conversely,â€¦ (More)

where B and D are square blocks. We prove the following inequalities for the Schatten q-norm ||.||q , which are sharp when the blocks are of size at least 2 Ã— 2: ||A||q â‰¤ (2 q âˆ’ 2)||C||q + ||B|| q qâ€¦ (More)

For real n-dimensional vectors x and y, we say that x is weakly majorised by y, denoted x â‰ºw y, if and only if for k = 1, . . . , n, âˆ‘k i=1 x â†“ i â‰¤ âˆ‘k i=1 y â†“ i . We say that x is majorised by y,â€¦ (More)

We convert a conjectured inequality from quantum information theory, due to He and Vidal, into a block matrix inequality and prove a very special case. Given n matrices Ai, i = 1, . . . , n, of theâ€¦ (More)