We extend the concept of the negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase under local quantum operations and classical communication, and derive explicit formulae for the entanglement measure of isotropic states and Werner states, applying the formalism presented by Vollbrecht and Werner [Phys. Rev. A 64, 062307 (2001)].

We introduce the concentrated information of tripartite quantum states. For three parties Alice, Bob, and Charlie, it is defined as the maximal mutual information achievable between Alice and Charlie via local operations and classical communication performed by Charlie and Bob. We derive upper and lower bounds to the concentrated information, and obtain a closed expression for it on several classes of states including arbitrary pure tripartite states in the asymptotic setting. We show that distillable entanglement, entanglement of assistance, and quantum discord can all be expressed in terms of the concentrated information, thus revealing its role as a unifying informational primitive. We finally investigate quantum state merging of mixed states with and without additional entanglement. The gap between classical and quantum concentrated information is proven to be an operational figure of merit for mixed state merging in the absence of additional entanglement. Contrary to the pure state merging, our analysis shows that classical communication in both directions can provide an advantage for merging of mixed states.

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We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular, we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.

We define an entanglement measure, called the partial tangle, which represents the residual twoqubit entanglement of a three-qubit pure state. By its explicit calculations for three-qubit pure states, we show that the partial tangle is closely related to the faithfulness of a teleportation scheme over a three-qubit pure state. PACS numbers: 03.67.-a, 03.65.Ud, 03.67.Mn 03.67.Hk,Quantum entanglement has been considered to be one of the most crucial resources in quantum information processing, and hence has been studied intensively in various ways. Nevertheless, there are still a number of open problems for entanglement, such as what is the best way to quantify the amount of entanglement for bipartite or multipartite states.For two-qubit states, the Wootters' concurrence C [1, 2, 3], is known as a good measure of entanglement, since from it we can directly derive the explicit formula for the entanglement of formation as well as being readily calculable. On the other hand, in the multi-qubit cases, or even in the three-qubit case, no entanglement measure as good as the concurrence of two qubits has been found yet.Coffman et al. [4] presented an inequality to explain the relation between bipartite entanglement in a three-qubit pure state. The inequality is called the Coffman-Kundu-Wootters (CKW) inequality, which iswhere C 12 = C(tr 3 (Ψ 123 )), C 13 = C(tr 2 (Ψ 123 )), and C 1(23) = C(Ψ 1(23) ) = 2 det(tr 23 (Ψ 123 )) for a three-qubit pure state Ψ 123 = |ψ 123 ψ|. Here, the subscripts represent the indices of the qubits. From the CKW inequality, an entanglement measure for three-qubit pure states was naturally derived [4,5]. It is called the 3-tangle τ , which is defined asand represents the residual entanglement of the state.Here τ is invariant under any qubit taken as the focus qubit, that is, for any distinct i, j, and k in {1, 2, 3},Furthermore, it was shown that τ is an entanglement monotone [5], and it was also shown that τ can distinguish the Greenberger-Horne-Zeilinger (GHZ) class from * Electronic address: level@khu.ac.kr † Electronic address: jaewoo.joo@imperial.ac.uk ‡ Electronic address: jaewan@kias.re.kr the W class [5], where the GHZ class and the W class are the sets of all pure states with true three-qubit entanglement equivalent to the GHZ state [6],under stochastic local operations and classical communication (SLOCC), and equivalent to the W state,under SLOCC, respectively. Even though the 3-tangle τ is a useful entanglement measure for three-qubit pure states, in this paper, we investigate another quantity similar to τ , defined asfor distinct i, j, and k in {1, 2, 3}. We call the quantity the partial tangle. Then we clearly obtain the following equalities:τ 12 = C 2 1(23) − C 2 13 = τ + C 2 12 = τ 21 , τ 23 = C 2 2(31) − C 2 21 = τ + C 2 23 = τ 32 ,and hence τ 2 12 + τ 2 23 + τ 2 31 = 3τ + C 2 12 + C 2 23 + C 2 31 .We clearly remark that τ ij = C ij if and only if a given state is contained in the W class, that is, τ = 0.Observing the definition of τ ij in Eq. (7), τ ij seems to represent the re...

Abstract. We exhibit a two-parameter class of states ρ (α,γ) , in 2 ⊗ n quantum system for n ≥ 3, which can be obtained from an arbitrary state by means of local quantum operations and classical communication, and which are invariant under all bilateral operations on 2 ⊗ n quantum system. We calculate the negativity of ρ (α,γ) , and a lower bound and a tight upper bound on its entanglement of formation. It follows from this calculation that the entanglement of formation of ρ (α,γ) cannot exceed its negativity.

We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In this paper, we show that our hybrid algorithm can reduce a circuit depth from the original HHL algorithm by means of a classical information feed-forward after the quantum phase estimation algorithm, and the results of the hybrid algorithm are identical to those of the HHL algorithm. In addition, it is experimentally examined with four qubits in the IBM Quantum Experience setups, and the experimental results of our algorithm show higher accurate performance on specific systems of linear equations than that of the HHL algorithm.

In this paper, we present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005), quant-ph/0506203] have nonzero distillable key rate, and finally exhibit new classes of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of distillable key rate for the ccq states of their privacy squeezed versions.