We present a direct relation, based upon a monogamic principle, between entanglement of formation (EOF) and quantum discord (QD), showing how they are distributed in an arbitrary tripartite pure system. By extending it to a paradigmatic situation of a bipartite system coupled to an environment, we demonstrate that the EOF and the QD obey a conservation relation. By means of this relation we show that in the deterministic quantum computer with one pure qubit the protocol has the ability to rearrange the EOF and the QD, which implies that quantum computation can be understood on a different basis as a coherent dynamics where quantum correlations are distributed between the qubits of the computer. Furthermore, for a tripartite mixed state we show that the balance between distributed EOF and QD results in a stronger version of the strong subadditivity of entropy.the pure qubit and the mixed ones [4]. Arguably, the power of the quantum computer is supposed to be related to QD, rather than entanglement [6]. Here, using the conservation relation, we have shown that even in the supposedly entanglement-free quantum computation there is a certain amount of multipartite entanglement between the qubits and the environment, which is responsible for the non-zero QD (See Fig. 1).

We study heat transport in a pair of strongly coupled spins. In particular, we present a condition for optimal rectification, i.e., flow of heat in one direction and complete isolation in the opposite direction. We show that the strong-coupling formalism is necessary for correctly describing heat flow in a wide range of parameters, including moderate to low couplings. We present a situation in which the strong-coupling formalism predicts optimal rectification whereas the phenomenological approach predicts no heat flow in any direction, for the same parameter values. [11,12]. It opens perspectives in quantum information processing, motivating studies on light-matter interaction at the single-photon level [13][14][15][16][17]. In analogy to modern electronic circuits, quantum devices have been proposed such as photon diodes [18,19] and photon transistors [20,21]. Diodes are current rectifiers. An optimal rectifier is able to conduct current in one sense and isolate it in the opposite sense.All such realistic quantum systems are, of course, open. Natural atoms interact with electromagnetic environments [22]. Artificial atoms also interact with their solidstate environment. There is the need to understand, at the single-quantum level, for instance, the influence of temperature [23][24][25] and of phonons [26,27], fluctuating charges [28], nuclear or electronic spins [29]. Analogies to diodes and transistors are also extendable to the flow of all such complex excitations [30].Manipulation of individual quantum systems also gave birth to engineered interactions between those systems [31]. In particular, ultra-strong couplings are achieved, e.g., between a two-level system and a single-mode cavity in circuit QED [32], totally modifying standard quantum optical scenarios [33].In this paper, we explore heat transport under the influence of strong coupling between spins. We argue that the strong-coupling formalism is necessary even for moderate and low couplings. We treat a case where optimal rectification is expected within the strong-coupling description and is completely absent for the standard phenomenological approach. Optimal rectification is evidenced by the system of two spins coupled via Ising interaction. A broad range of experiments is capable of reproducing Ising-type interactions, simulating spins in the strong-coupling regime [34].Model. The system of interest consists in a pair of interacting spins. We define the coupling constant ∆ between the spins in the z-direction. The magnetic field h applied to the spin on the left is also in the z-direction. The Hamiltonian of the system isThe spin on the left (right) is coupled with a thermal reservoir at a given temperature T L (T R ). The system is illustrated in Figure 1(a). The four eigenstates of H S are given in terms of the eigenstates of σ, | ↑ and | ↓ , in decreasing energy order for the case of interest, ∆ < h, |4 = | ↑↑ , |3 = | ↑↓ , |2 = | ↓↓ , |1 = | ↓↑ We define the transition frequencies as ω mn = m − n , where k is the eigenvalue of H S for the eig...

We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.

It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.

Quantum discord (QD) measures the fraction of the pairwise mutual information that is locally inaccessible in a multipartite system. Fundamental aspects related to two important measures in quantum information theory, namely the entanglement of formation (EOF) and the conditional entropy, can be understood in terms of the distribution of this form of local inaccessible information (LII). As such, the EOF for an arbitrarily mixed bipartite system AB can be related to the gain or loss of LII due to the extra knowledge that a purifying ancillary system E has on the pair AB. Similarly, a clear meaning of the negativity of the conditional entropy for AB is given. We employ these relations to elucidate important and yet not well-understood quantum features, such as the bipartite entanglement sudden death and the distinction between EOF and QD for quantifying quantum correlation. For that we introduce the concept of LII flow that quantifies the LII shared in a multipartite system when sequential local measurements are carried out.