Abstract:
How does the amplitude of a wiggle on a string change when the string is stretched? We answer this question for both longitudinal and transverse wiggles and for arbitrary equation of state, {\it i.e.}, for arbitrary relation between the tension $\tau$ and the energy per unit length $\epsilon$ of the string. This completes our derivation of the renormalization of string parameters which results from averaging out small scale wiggles on a string. The program is presented here in its entirety.

Abstract:
We derive a class of inequalities, from the uncertainty relations of the SU(1,1) and the SU(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su(2) operators J_x, J_y, and the total photon number N_a+N_b. They include as special cases the inequality derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas [New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Biswas. We show that this optimal criterion can detect entanglement for a broad class of non-Gaussian entangled states, i.e., the su(2) minimum-uncertainty states. Experimental schemes to test the optimal criterion are also discussed, especially the one using linear optical devices and photodetectors.

Abstract:
We study entanglement of electron spins in many-body systems based on the Green's function approach. As an application we obtain the two-particle density matrix of a non-interacting electron gas and identify its two-spin density matrix as a Werner state. We calculate entanglement measures, a classical correlation, mutual information, and a pair distribution function of two electrons at zero and finite temperatures. We find that changes of entanglement measures are proportional to $T^2$ at low temperatures.

Abstract:
Schemes for generation and protocols for network teleportation of multimode entangled cat-states are proposed. Explicit expressions for probability of successful teleportation are derived for both symmetric and asymmetric networks.

Abstract:
We investigate entanglement of two electron spins forming Cooper pairs in an s-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not the order of the coherence length but the order of the Fermi wave length.

Abstract:
Based on Yosida's ground state of the single-impurity Kondo Hamiltonian, we study three kinds of entanglement between an impurity and conduction electron spins. First, it is shown that the impurity spin is maximally entangled with all the conduction electrons. Second, a two-spin density matrix of the impurity spin and one conduction electron spin is given by a Werner state. We find that the impurity spin is not entangled with one conduction electron spin even within the Kondo screening length $\xi_K$, although there is the spin-spin correlation between them. Third, we show the density matrix of two conduction electron spins is nearly same to that of a free electron gas. The single impurity does not change the entanglement structure of the conduction electrons in contrast to the dramatic change in electrical resistance.

Abstract:
We present two linear optical schemes using nonideal photodetectors to demonstrate inseparability of W-type N-partite entangled states containing only a single photon. First, we show that the pairwise entanglement of arbitrary two modes chosen from N optical modes can be detected using the method proposed by Nha and Kim [Phys. Rev. A 74, 012317 (2006)], thereby suggesting the full inseparability among N parties. In particular, this scheme is found to succeed for any nonzero quantum efficiency of photodetectors. Second, we consider a quantum teleportation network using linear optics without auxiliary modes. The conditional teleportation can be optimized by a suitable choice of the transmittance of the beam splitter in the Bell measurement. Specifically, we identify the conditions under which maximum fidelity larger than classical bound 2/3 is achieved only in cooperation with other parties. We also investigate the case of on-off photodetectors that cannot discriminate the number of detected photons.

Abstract:
We study a system of two qubits interacting with a common environment, described by a two-spin boson model. We demonstrate two competing roles of the environment: inducing entanglement between the two qubits and making them decoherent. For the environment of a single harmonic oscillator, if its frequency is commensurate with the induced two-qubit coupling strength, the two qubits could be maximally entangled and the environment could be separable. In the case of the environment of a bosonic bath, the gap of its spectral density function is essential to generate entanglement between two qubits at equilibrium and for it to be used as a quantum data bus.

Abstract:
Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and entanglement, and then characterize the non-classicality that precisely corresponds to entanglement. The results naturally follow from two findings: one is the general structure among non-classical, entangled, separable, and classical states over Hermitian operators, and the other a general scheme to detect non-classical states.

Abstract:
Detecting nonclassical properties that do not allow classical interpretation of photoelectric counting events is one of the crucial themes in quantum optics. Observation of individual nonclassical effects for a single-mode field, however, has been so far practically confined to sub-Poissonian statistics and quadrature squeezing. We show that a photon-added classical (coherent or thermal) state exhibits generalized nonclassical features in all orders of creation and annihilation operators, thereby becoming a promising candidate for studying higher-order nonclassical effects. Our analysis demonstrates robustness of these effects against nonideal experimental conditions.