I. INTRODUCTION It is well known that entanglement of quantum states is an important physical resource in the context of the quantum information theories. It plays a crucial role in quantum teleportation[1], superdense coding[2], quantum cloning[3], quantum cryptography[4] and quantum computer technology[5, 6] $^{1}$. Therefore, to understand how to quantify and how to characterize the entanglement for a given quantum state is an highly important physical task. Many entanglement measures have been developed for last few years. Above all, in our opinion, the most important entanglement measure is a distillable entanglement[10], which quantifies how many maximally entangled states can be constructed from the copies of the given quantum state in the asymptotic region. The importance of the distillable entanglement arises due to the fact that the entanglement is fragile when noises interfere the quantum information processing. The disadvantage of the distillable entanglement is its calculational difficulty. In order to compute the distillable entanglement analytically we should find the optimal purification (or distillation) protocol. If this optimal protocol generates n maximally entangled states from m -copies of the quantum state ρ , the distillable entanglement for ρ is given by 2 However, finding an optimal purification protocol is an highly non-trivial task. It makes it difficult to compute the distillable entanglement analytically. Fortunately, the tight upper bound of the distillable entanglement has been developed in Ref.[11, 12]. In these references the new entanglement measure called relative entropy of entanglement (REE) was introduced. It is defined as D ( ρ ) = lim m →∞ n m . (1.1) E$_{R}$ ( ρ ) = min σ ∈D S ( ρ || σ ) , (1.2) 1 There are, however, several examples, where entanglement does not play an important role in the quantum computation. For example, the efficiency of Grover’s search algorithm gets worsened if the initial state is entangled one[7]. Another important example is a deterministic quantum computation with one pure qubit[8]. Other simple examples are presented in Ref.[9]. Therefore, one cannot conclude definitely that entanglement is essential for quantum computation. 2 In Ref.[10] the distillable entanglement D is divided into D$_{1}$ and D$_{2}$ depending on one-way and two-way classical communications. Throughout this paper we only consider the two-way classical communication. 2