Entanglement witnesses of four-qubit tripartite separable quantum states

A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Comparing to the entanglement of bipartite quantum systems, less progresses have been made for the entanglement of multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, it is proved that the necessary conditions of tripartite separability are also sufficient at W state side.

Generalized Holographic Principle, Gauge Invariance and the Emergence of Gravity à la Wilczek

We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincaré group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast à la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the representation theory of the Lie groups SO(3,2) and SO(4,1).

Correlation minor norms, entanglement detection and discord

In this paper we develop an approach for detecting entanglement, which is based on measuring quantum correlations and constructing a correlation matrix. The correlation matrix is then used for defining a family of parameters, named Correlation Minor Norms, which allow one to detect entanglement. This approach generalizes the computable cross-norm or realignment (CCNR) criterion, and moreover requires measuring a state-independent set of operators. Furthermore, we illustrate a scheme which yields for each Correlation Minor Norm a separable state that maximizes it. The proposed entanglement detection scheme is believed to be advantageous in comparison to other methods because correlations have a simple, intuitive meaning and in addition they can be directly measured in experiment. Moreover, it is demonstrated to be stronger than the CCNR criterion. We also illustrate the relation between the Correlation Minor Norm and entanglement entropy for pure states. Finally, we discuss the relation between the Correlation Minor Norm and quantum discord. We demonstrate that the CMN may be used to define a new measure for quantum discord.

Entangling Superconducting Qubits through an Analogue Wormhole

We propose an experimental setup to test the effect of curved spacetime upon the extraction of entanglement from the quantum field vacuum to a pair of two-level systems. We consider two superconducting qubits coupled to a dc-SQUID array embedded into an open microwave transmission line, where an external bias can emulate a spacetime containing a traversable wormhole. We find that the amount of vacuum entanglement that can be extracted by the qubits depends on the wormhole parameters. At some distances qubits which would be in a separable state in flat spacetime would become entangled due to the analogue wormhole background.

Quantum entanglement purification assisted by classical phase noise

Entanglement purification is a vital protocol to produce a high-quality entangled state from an ensemble of identical states. Based on the particular scheme of entanglement purification [Phys. Rev. A 87, 052316 (2013)], the effect of phase fluctuation is investigated. The convergence pattern of the initial states can be divided into two kinds of regions, corresponding to the purified outcomes being a maximally entangled state (MES) or a separable state. And there is the fractal-like structure near the boundary between these two regions. It is found that the phase noise plays a positive role in generating an MES for an initial states near some fractal boundary, which can only become the separable one if the noise is absent. It is also found that the minimal iteration steps to achieve the maximally entangled state with the phase noise can be decreased, which can save the resource in the protocol.

Distance between Bound Entangled States from Unextendible Product Bases and Separable States

We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendible product basis bound entangled states (UPB BE states). The method relies on the fact that an optimal entanglement witness is given by a plane perpendicular to a line between the reference state, entanglement of which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds an approximation of CSS. In this article, we investigate if this approximation can be good enough to yield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those given by Bandyopadhyay–Ghosh–Roychowdhury (BGR) construction. This comparison allows us to learn about the amount of entanglement and we find a relationship between it and a feature of the construction of UPBBE states, namely the size of their central tile. We show that in most studied cases, witnesses found with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay, Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections in a realization of the state.

Magnetic resonance with number states versus coherent states

In this paper, we study the interaction of quantized radio-frequency (rf)/microwave-field with nuclear spin in Nuclear Magnetic Resonance (NMR) or electron spin in Electron Paramagnetic Resonance (EPR). In magnetic resonance experiments, interaction of quantized rf-field leads to entanglement of spin with the electromagnetic field. In an entangled state, the spins are depolarized with no net transverse magnetization, which cannot give a detectable signal in inductive detection (or Q detection) that detects transverse magnetization. We show that when the electromagnetic field is in coherent state, inductive detection becomes possible. We use the mathematics of quantum optics to study the evolution of a coherent rf-field with a sample of all polarized spins. We show that evolution can be solved in closed form as a separable state of rf-field and spin ensemble, where spin ensemble evolves according to Bloch equations in an rf-field. We extend the analysis and results to a spin ensemble with Boltzmann polarization. The rabi frequency and coupling strength of spins to rf-field depends on number state of the rf-field. We show that in interaction with a coherent rf-field, this variation in coupling strength introduces negligible error.