No abstract

Abstract. Using Rényi-α entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for α ≥ 2. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for 0.83 − ǫ ≤ α ≤ 1.43 + ǫ with 0 < ǫ < 0.01.

We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MoE). We show that all proven MoE relations using concurrence can be rephrased in terms of CREN. Furthermore we show that higher-dimensional (qudit) extensions of MoE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MoE in terms of concurrence. We further test the CREN version of MoE for qudits by considering fully or partially coherent mixtures of a qudit W-class state with the vacuum and show that the CREN version of MoE for qudits is satisfied in this case as well. The CREN version of MoE for qudits is thus a strong conjecture with no obvious counterexamples.

Abstract. We show that restricted shareability of multi-qubit entanglement can be fully characterized by unified-(q, s) entropy. We provide a two-parameter class of bipartite entanglement measures, namely unified-(q, s) entanglement with its analytic formula in two-qubit systems for q ≥ 1, 0 ≤ s ≤ 1 and qs ≤ 3. Using unified-(q, s) entanglement, we establish a broad class of the monogamy inequalities of multi-qubit entanglement for q ≥ 2, 0 ≤ s ≤ 1 and qs ≤ 3.

While quantum entanglement is known to be monogamous (i.e. shared entanglement is restricted in multi-partite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multi-qubit systems, and several trade offs between UE and other correlation measures.