Quantum entanglement can manifest itself in the narrowing of wavepackets. We define the phenomenon of phase entanglement and describe its effect on the interpretation of spatial localization experiments.
We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds facilitate estimates of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures.
We investigate the features of the entanglement spectrum (distribution of the eigenvalues of the reduced density matrix) of a large quantum system in a pure state. We consider all Renyi entropies and recover purity and von Neumann entropy as particular cases. We construct the phase diagram of the theory and unveil the presence of two critical lines.
The topological phase factor induced on interfering electrons by external quantum electromagnetic fields has been studied. Two and three electron interference experiments inside distant cavities are considered and the influence of correlated photons on the phase factors is investigated. It is shown that the classical or quantum correlations of the irradiating photons are transferred to the topological phases. The effect is quantified in terms of Weyl functions for the density operators of the photons and illustrated with particular examples. The scheme employs the generalized phase factor as a mechanism for information transfer from the photons to the electric charges. In this sense, the scheme may be useful in the context of flying qubits (corresponding to the photons) and stationary qubits (electrons), and the conversion from one type to the other.
We study the generation of planar quantum squeezed (PQS) states by quantum non-demolition (QND) measurement of a cold ensemble of $^{87}$Rb atoms. Precise calibration of the QND measurement allows us to infer the conditional covariance matrix describing the $F_y$ and $F_z$ components of the PQS, revealing the dual squeezing characteristic of PQS. PQS states have been proposed for single-shot phase estimation without prior knowledge of the likely values of the phase. We show that for an arbitrary phase, the generated PQS gives a metrological advantage of at least 3.1 dB relative to classical states. The PQS also beats traditional squeezed states generated with the same QND resources, except for a narrow range of phase values. Using spin squeezing inequalities, we show that spin-spin entanglement is responsible for the metrological advantage.
We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A Hamiltonian is constructed from the unitary $check{R}_{i,i+1}(theta,phi)$-matrix, where $phi=omega t$ is time-dependent while $theta$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.