Disentangling theorem and monogamy for entanglement negativity

Monogamy of Correlations vs. Monogamy of Entanglement

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even...

Disentangling entanglement

On a Block Matrix Inequality quantifying the Monogamy of the Negativity of Entanglement

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 ...

General monogamy inequality for bipartite qubit entanglement.

We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy inequality to the concept of frustration of correlations in quantum spin systems.

Monogamy and entanglement in tripartite quantum states

We present an interesting monogamy equation for (2⊗ 2⊗ n)-dimensional pure states, by which a quantity is found to characterize the tripartite entanglement with the GHZ type and W type entanglements as a whole. In particular, we, for the first time, reveals that for any quantum state of a pair of qubits, the difference between the two remarkable entanglement measures, concurrence and negativity...