nt - p h / 05 05 20 1 v 1 26 M ay 2 00 5 Extracting an arbitrary relative phase from a multiqubit two - component entangled state

Entanglement plays an important role in quantum information processing and communication, such as quantum computation, secret sharing, teleportation, and quantum key distribution [1-3]. Over the last decade, characterizing or/and quantifying entanglement has been recognized as one of central tasks in quantum information science. Correspondingly, there have been many efforts in this direction, for both pure and mixed states as well as for bipartite and multipartite systems. These include entanglement of formation [4], entanglement of distillation [5], relative entropy of entanglement [6], negativity [7], geometric measure of entanglement [8], and so on. On the other hand, there is a strong current interest in the detection of quantum entanglement. To verify whether a qubit system is indeed prepared in a desired entangled state, many methods for the entanglement detection have been presented. Among them, there are proposals based on the structural approximations [9], the semidefinite program [10], and the entanglement witnesses [11-14]. In addition, the idea of inferring quantum entanglement using a single measurement basis has been proposed by Schelpe et. al. recently [15]. Quantum states can encode information (e.g., by amplitude, phase, or both) that may only be extracted by analyzing the states as a whole. Stimulated by the rapid development in quantum communication and quantum cryptography, the question of how to determine the actual state of a quantum system has gained renewed interest. Recently, a large number of significant schemes for diagnosing the states of a system have been proposed based on the quantum tomography technique (i.e., reconstruction of the states by measuring enough observables, given many copies of a quantum state) [16]. However, for some solid state qubit systems, it is very difficult to implement quantum tomography since usually very few, if not just one, observables can be measured. In this work, we propose a method for extracting the relative phase of a n-qubit two-component entangled state with the general form of √ p |i1i2...in〉+ e √