On a Block Matrix Inequality quantifying the Monogamy of the Negativity of Entanglement
نویسنده
چکیده
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 the same size, let Z1 and Z2 be the block matrices Z1 := (AjA ∗ i ) n i,j=1 and Z2 := (A ∗ jAi) n i,j=1. Then the conjectured inequality is (||Z1||1 − TrZ1) + (||Z2||1 − TrZ2) ≤ ∑ i̸=j ||Ai||2||Aj ||2 2 , where || · ||1 and || · ||2 denote the trace norm and the Hilbert-Schmidt norm, respectively. We prove this inequality for the already challenging case n = 2 with A1 = I.
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