Abstract
A conjecture from the distillability of quantum entanglement is that when A and B are 4×4 trace zero complex matrices and ‖A‖2+‖B‖2=1/4 (where ‖⋅‖ is the Frobenius norm), the sum of squares of the largest two singular values of A⊗I4+I4⊗B does not exceed 1/2. In this paper, the conjecture is proved when(i)A or B is unitarily similar to a direct sum of 2×2 trace zero matrices;(ii)A and B are unitarily similar to matrices, when partitioned into 2×2 blocks, having zero diagonal blocks.
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