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We introduce the challenges of multi-party quantum entanglement and explain a recent success in learning to take its measure. Given the widely accepted reputation of entanglement as a counter-intuitive feature of quantum theory, we first describe pure-state entanglement itself. We restrict attention to multi-party qubit states. Then we introduce the features that have made it challenging for several decades to extend an entanglement measure beyond the 2-qubit case of Bell states. We finish with a description of the current understanding that solves the 3-qubit entanglement challenge. This necessarily takes into account the fundamental division of the 3-qubit state space into two completely independent sectors identified with the so-called GHZ and $W$ states., 16 pages and 3 figures

Entanglement freezing has been demonstrated existing in various noisy decoherence mechanisms. Here we explore its universality by investigating freezing behavior in a lossless multiparty system, i.e., an $N$-site optical lattice (or equivalently spin-chain) system. Interesting phenomenon of permanent entanglement freezing is found for the infinite-size case ($N\rightarrow\infty$). As the multiparty system size reduces to finite $N$, the interesting behavior of dynamical entanglement "thawing" start to emerge. Especifically, alternative appearances of "freezing" and "thawing" can be identified as time evolves. Our results may provide useful guidance to entanglement control in quantum tasks., Comment: 6 pages

We extend our earlier "virtual detector" method [X. Wang, J. Tian, and J. H. Eberly, Phys. Rev. Lett. 110, 243001 (2013)], a hybrid quantum mechanical and classical trajectory method, to include phases in the classical trajectories. Effects of quantum interferences, lost in the earlier method, are restored. The obtained photoelectron momentum distributions agree well with the corresponding numerical solutions of the time-dependent Schr\"odinger equation.

Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness., Comment: 8 pages, 4 figures

We investigate the effects of error correction on non-local quantum coherence as a function of time, extending the study by Sainz and Bj\"ork. We consider error correction of amplitude damping, pure phase damping and combinations of amplitude and phase damping as they affect both fidelity and quantum entanglement. Initial two-qubit entanglement is encoded in arbitrary real superpositions of both \Phi-type and \Psi-type Bell states. Our main focus is on the possibility of delay or prevention of ESD (early stage decoherence, or entanglement sudden death). We obtain the onset times for ESD as a function of the state-superposition mixing angle. Error correction affects entanglement and fidelity differently, and we exhibit initial entangled states for which error correction increases fidelity but decreases entanglement, and vice versa., Comment: 10 pages, 10 figures; references added; journal reference added

Multielectron double ionization with elliptically polarized light is examined theoretically using a classical ensemble method going beyond the single-active-electron approximation. A knee structure in the ion signal is found. Our analysis provides an explanation for newly observed SDI phenomena.

The entanglement dynamics of two remote qubits is examined analytically. The qubits interact arbitrarily strongly with separate harmonic oscillators in the idealized degenerate limit of the Jaynes-Cummings Hamiltonian. In contrast to well known non-degenerate RWA results, it is shown that ideally degenerate qubits cannot induce bipartite entanglement between their partner oscillators., Comment: 8 pages, 6 figures

The prospect of self-consistent propagation of more than two pulses contemporaneously through multi-resonant media raises open questions: whether soliton solutions exist, and whether a useful generalization of two-level pulse Area can be found. We answer these questions positively for the case of four pulses interacting in combined V and Lambda fashion with an idealized pair of atomic D-lines., Comment: 4 pages, 3 figures