Entanglement of formation of pair of quantum dots Sergio Sánchez S.* a,b , J. J. Sánchez Mondragón a , J. C. García Melgarejo a , A. Alejo-Molina a a Dept. of Optics, National Institute of Astrophysics Optics and Electronics (INAOE) Tonatzintla Puebla, México; b Institute of Energy Studies (IEE), in University of Isthmus, (UNISTMO) Tehuantepec Oaxaca, México. ABSTRACT The Entanglement of quantum systems is a key aspect in order to understand the dynamics and behavior of mixed systems (density matrix) as bipartite systems of quantum bits (q-bits). A quantifiable measure widely used is the “entanglement of formation” of a mixed state, defined as the minimum number of singlets needed to create an ensemble of pure states that represents the density matrix of the system. Considering a double quantum dot system coupled cavity type Jaynes-Cummings investigate the entanglement between two quantum dots, immersed each in its own cavity, showing analytically that entanglement has a very interesting effects such as temporal evolution including the so-called sudden death effect. Keywords: Entanglement, quantum-bits, concurrence, quantum dots 1. INTRODUCTION For several years a lot of authors have studied the entanglement due to its immense importance not only at the fundamental level but also for purposes of applications to quantum information and quantum computing [1]. Entanglement has marked a new way to reinterpret the quantum nature of computer technology due to the incorporation of quantum processing units with so-called quantum bits (q-bits), represented as dual units that open up infinite possibilities for processes parallel at least theoretically much faster any classical computational process. However this has been the case at the theoretical level so it is essential to implement physical models that allow the incorporation of this development. Therefore a precise measurement is needed to quantify the degree of entanglement for such system of q-bits. Thus quantum entanglement has played very important roles in quantum information processing such as quantum teleportation, [1, 2] quantum cryptographic, [3] quantum dense coding,[4] and parallel computing [5]. However the physical character and mathematical structure of entangled states have not been well understood. There are two important problems for entanglement. One is to find a method to determine whether a given state is separable (or not entangled), and the other is to define the best measure quantifying an amount of entanglement of a given state. In order to solve the first problem, much effort has been made. [6-8]. The quest for proper measures of entanglement has received a great deal of attention. The entanglement of formation, distillation, and relative entropy, [9-11] negativity, [12] concurrence, [12, 13] concurrence related measures, or positive operator are used to investigate entanglement. Although the entanglement of formation is defined for arbitrary-dimensional bipartite systems, so far no explicit analytic formulates for entanglement of formation have been found for systems larger than a pair of qubits, except for some special symmetric states. [14] . Another serious problem that must be considered in entanglement as mentioned earlier in a quantum system is it may deteriorate due to interaction with background noise or with other systems usually called environments. Interest was originally concerned with the consequences for quantum measurement and the quantum-classical transition [15–17]. More recently, entanglement decoherence has been studied in connection with obstacles to realizing various quantum information processing schemes. T. Yu and Eberly have shown that entanglement can decay to zero abruptly, in a finite time, a phenomenon termed entanglement sudden death [18, 19]. Such quantum correlations are responsible for much of the challenge in understanding interacting many-body quantum systems, and it is therefore of fundamental importance to have quantitative knowledge of these correlations. Progress in 22nd Congress of the International Commission for Optics: Light for the Development of the World, edited by Ramón Rodríguez-Vera, Rufino Díaz-Uribe, Proc. of SPIE Vol. 8011, 801140 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.903406 Proc. of SPIE Vol. 8011 801140-1