Entanglement concentration of individual photon pairs via linear optical logic

Entanglement has played a key role in many quantum information processing, such as quantum computation [1], quantum teleportation [2], quantum dense coding [3], and entanglement-assisted quantum cryptography [4]. To function optimally these applications requires maximally entanglement. However, unwanted coupling to the environment causes the degradation of entanglement and entanglement concentration [5] is thus essential for quantum computing. The basic idea of entanglement concentration is to distill some pairs of particles in highly entangled states from less entangled states using local quantum operations and two-way classical communications (LOCC) [1]. In practice, there are two fundamentally different types of concentration protocols: those acting on individual pairs of entangled particles [6] and those acting collectively on many pairs [7]. In recent years, entanglement concentration using linear optical elements has received much attention [8, 9, 10]. In the case of concentration of individual entanglement photon pairs, Thew and Munro proposed a protocol based on beam splitters with variable transmission coefficients (VBS) [9] and experimentally, Kwiat et. al. has implemented individual entanglement concentration using partial polarizers [10]. However, both Thew and Munro’s protocol and Kwiat’s experiment included parameters that are difficult to adjust in practice: Thew and Munro’s scheme requires four VBS and the partial polarizers in Kwiat’s experiment must be changed according to the initial entanglement. In this paper, we propose a scheme for concentrating nonmaximally pure and mixed polarization-entangled state of individual photon pairs using linear optical elements (polarization beam splitter (PBS), half wave plate (HWP), and quarter wave plate (QWP)) . The scheme uses only Mach-Zehnder interferometers and a few adjustable polarization rotations (generated by HWP and QWP) and maybe greatly simplify the experiment. The crucial part in any individual pairs’ entanglement concentration scheme is the realization of single-qubit local quantum operator, including unitary rotation and the positive-operator-valued measurement (POVM) [11]. Generally, a single-qubit unitary rotation on the polarization of a photon (or single-qubit polarization rotation (SPR)) has the