Jeong San Kim

Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity

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

Generalized W-Class State and its Monogamy Relation

W

Tsallis entropy and entanglement constraints in multiqubit systems

-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.

Monogamy of multi-qubit entanglement using Rényi entropy

We generalize the W-class of states from n-qubits to n-qudits and prove that their entanglement is fully characterized by their partial entanglements even for the case of the mixture that consists of a W-class state and a product state .

Unified entropy, entanglement measures and monogamy of multi-party entanglement

We show that the restricted shareability and distribution of multiqubit entanglement can be characterized by Tsallis-q entropy. We first provide a class of bipartite entanglement measures named Tsallis-q entanglement, and provide its analytic formula in two-qubit systems for 1{<=}q{<=}4. For 2{<=}q{<=}3, we show a monogamy inequality of multiqubit entanglement in terms of Tsallis-q entanglement, and we also provide a polygamy inequality using Tsallis-q entropy for 1{<=}q{<=}2 and 3{<=}q{<=}4.

Limitations to sharing entanglement

We introduce a class of bipartite entanglement measures based on Renyi-α entropy, namely Renyi-α entanglement with an analytic formula in two-qubit systems for α ≥ 1. We also show that multi-qubit entanglement has a monogamy inequality in terms of Renyi-α entanglement for all α ≥ 2.

Quantum states for perfectly secure secret sharing

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.

Polygamy of entanglement in multipartite quantum systems

We discuss limitations to sharing entanglement known as monogamy of entanglement. Our pedagogical approach commences with simple examples of limited entanglement sharing for pure three-qubit states and progresses to the more general case of mixed-state monogamy relations with multiple qudits.

Distribution and dynamics of entanglement in high-dimensional quantum systems using convex-roof extended negativity

In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.

Monogamy of multi-qubit entanglement in terms of Rényi and Tsallis entropies

We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytic upper bound for the concurrence of assistance in bipartite quantum systems, and derive a polygamy inequality of multipartite entanglement in arbitrary dimensional quantum systems.