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).

The degree of non-Markovianity of quantum processes has been characterized in several different ways in the recent literature. However, the relationship between the non-Markovian behavior and the flow of information between the system and the environment through an entropic measure has not been yet established. We propose an entanglement-based measure of non-Markovianity by employing the concept of assisted knowledge, where the environment E, acquires information about a system S, by means of its measurement apparatus A. The assisted knowledge, based on the accessible information in terms of von Neumann entropy, monotonically increases in time for all Markovian quantum processes. We demonstrate that the signatures of non-Markovianity can be captured by the nonmonotonic behavior of the assisted knowledge. We explore this scenario for a two-level system undergoing a relaxation process, through an experimental implementation using an optical approach that allows full access to the state of the environment. The inevitable interaction between a system and its environment typically results in the loss of quantum features, such as coherence [1,2]. One important aspect in the study of these so-called open quantum systems is the concept of non-Markovianity, which arises due to memory effects of the environment. Non-Markovian features might enable the system to recover part of the lost coherence and information back from the environment [1][2][3][4]. Although these memory effects have been investigated in the past, only recently an increase in the understanding of nonMarkovianity from a quantum information perspective has emerged [5][6][7][8][9][10][11].The non-Markovian nature of a dynamical quantum map can be characterized through a number of distinct methods [5][6][7][8][9][10]. To date, the measure defined by Breuer, Laine, and Piilo [6] based on trace distance, is the most significant quantifier of the degree of non-Markovianity, due to its interpretation: non-Markovianity manifests itself as a reverse flow of information from the environment back to the system. An alternative method to measure the degree of non-Markovianity relies on the fact that local, completely positive trace-preserving (CPTP) maps cannot increase the entanglement between an open quantum system and an isolated ancillary system [12]. Exploiting this property, Rivas, Huelga, and Plenio (RHP) have defined another measure for the degree of non-Markovianity [7]. According to the RHP measure, a dynamical process is said to be nonMarkovian if the entanglement between the open system and the isolated ancilla temporarily increases throughout the dynamics. Although the RHP measure provides a connection between the non-Markovian behavior of dynamical maps and entanglement, a meaning in terms of information flow is still lacking in this approach.Here, we propose an entanglement-based measure of non-Markovianity having a direct information based interpretation. Our method is based on the decoherence program [13], where a system S is coupled to a measurement ...

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.

In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both regimes of weakly and strongly interacting oscillators from which interesting results arise concerning the coherence properties of the joint and the reduced system states. The strong coupling regime is required to achieve a large frequency shift of the oscillator normal modes, making it possible to explore the whole profile of the spectral density of the reservoirs. We show how the decoherence process may be controlled by shifting the normal mode frequencies to regions of small spectral density of the reservoirs. Different spectral densities of the reservoirs are considered and their effects on the decoherence process are analyzed. For oscillators with different damping rates, we show that the worse-quality system is improved and vice-versa, a result which could be useful for quantum state protection. State recurrence and swap dynamics are analyzed as well as their roles in delaying the decoherence process.

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-not (cnot). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 cnot gates, whereas ours only needs one, bringing it within the range of current experiments.

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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.