Sufficient Condition For Entanglement Research Articles

Correlations between outcomes of random measurements

We recently showed that multipartite correlations between outcomes of random observables detect quantum entanglement in all pure and some mixed states. In this followup article we further develop this approach, derive a maximal amount of such correlations, and show that they are not monotonous under local operations and classical communication. Nevertheless, we demonstrate their usefulness in entanglement detection with a single random observable per party. Finally we study convex-roof extension of the correlations and provide a closed-form necessary and sufficient condition for entanglement in rank-2 mixed states and a witness in general.

Operational approach to entanglement and how to certify it

Entangled physical systems are an important resource in quantum information. Many papers were published trying to grasp the meaning of entanglement. It was noticed that a Hilbert space of possible state vectors of compound physical system can be partitioned by introducing various tensor product structures induced by the experimentally accessible observables (interactions and measurements). In this sense, the entanglement is relative to a particular set of experimental capabilities. Inspired by these results some authors claim that in fact all quantum states are entangled. In this paper, we show that this claim is incorrect and we discuss in operational way differences existing between separable and entangled states. A sufficient condition for entanglement is the violation of Bell–CHSH-CH inequalities and/or steering inequalities. Since there exist experiments outside the domain of quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon. We also explain that an unambiguous experimental certification of the entanglement is a difficult task because classical statistical significance tests may not be trusted if sample homogeneity cannot be tested or is not tested carefully enough.

ENTANGLEMENT CRITERION FOR COHERENT SUBTRACTION AND COHERENT ADDITION OF BIPARTITE CONTINUOUS VARIABLE STATES

We study the entanglement conditions of two quite general classes of two-mode non-Gaussian states. Using computable cross norm and realignment criterion, we obtain the sufficient conditions of entanglement for coherently added or subtracted two-mode squeezed thermal states, and the sufficient condition of entanglement for any photon number entangled state (PNES) evolving in a thermal noise and amplitude damping channel.

Quantum Fisher Information in Two-Qubit Pure States

In terms of quantum Fisher information (QFI), a quantity χ 2 was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ 2<1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality χ 2<1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ 2 is equal to the second kind of spin squeezing parameter \(\xi _{2}^{2}\). For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition, we extend the concept of the QFI and χ 2, and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ 2 in symmetric pure states to arbitrary pure states.

Conditions for entanglement in multipartite systems

We introduce two entanglement conditions that take the form of inequalities involving expectation values of operators. These conditions are sufficient conditions for entanglement, that is if they are satisfied the state is entangled, but if they are not, one can say nothing about the entanglement of the state. These conditions are quite flexible, because the operators in them are not specified, and they are particularly useful in detecting multipartite entanglement. We explore the range of utility of these conditions by considering a number of examples of entangled states, and seeing under what conditions entanglement in them can be detected by the inequalities presented here.

Quantum entanglement in photosynthetic light-harvesting complexes

Light harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long time scales despite the decohering effects of their environments. Within this context, we analyze entanglement in multi-chromophoric light harvesting complexes, and establish methods for quantification of entanglement by presenting necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna-Matthews-Olson (FMO) protein to extract the initial state and temperature dependencies of entanglement. We show that while FMO in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement exists even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical utilization of entanglement in densely packed molecular aggregates such as light harvesting complexes.

Conditions for multipartite continuous-variable entanglement

Necessary and sufficient observable conditions for the nonnegativity of all partial transpositions of multi-mode quantum states are derived. The result is a hierarchy of inequalities for minors in terms of moments of the given state. Violations of any inequality is a sufficient condition for entanglement. Full entanglement can be certified for a manifold of multi-mode quantum states. A \textit{Mathematica} package is given for a systematic test of the hierarchy of conditions.

Inseparability Criteria for Continuous Bipartite Quantum States

We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under study. The violation of any inequality of this series is a sufficient condition for entanglement. Previously known entanglement conditions are shown to be special cases of our approach.

Entanglement detection based on interference and particle counting

A sufficient condition for entanglement in two-mode continuous systems is constructed with the interference visibility and the uncertainty of the total particle number. The observables to be measured (particle numbers and particle number variances) are relatively easily accessible experimentally. The method may be used to detect entanglement in light fields or in Bose-Einstein condensates. In contrast to the standard approach based on entanglement witnesses, the condition is expressed in terms of an inequality which is nonlinear in expectation values. The condition is constructed using uncertainty relations with the particle number and the destruction operators.

Some aspects of separability

We present three necessary separability criteria for bipartite mixed states; the violation of each of these conditions is a sufficient condition for entanglement. Some ideas on the issue of finding a necessary and sufficient criterion of separability are also discussed.

Optimization of entanglement witnesses

An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an optimal way. We show how to optimize general EW, and then we particularize our results to the non-decomposable ones; the latter are those that can detect positive partial transpose entangled states (PPTES). We also present a method to systematically construct and optimize this last class of operators based on the existence of ``edge'' PPTES, i.e. states that violate the range separability criterion [Phys. Lett. A{\bf 232}, 333 (1997)] in an extreme manner. This method also permits the systematic construction of non-decomposable positive maps (PM). Our results lead to a novel sufficient condition for entanglement in terms of non-decomposable EW and PM. Finally, we illustrate our results by constructing optimal EW acting on $H=\C^2\otimes \C^4$. The corresponding PM constitute the first examples of PM with minimal ``qubit'' domain, or - equivalently - minimal hermitian conjugate codomain.