Related papers: Minimal criteria for continuous-variable genuine m…
In this paper we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has…
Quantum universal invariants of a Gaussian state's covariance matrix, which can be derived from intensity correlation moments, have been adopted to characterize the entanglement properties of Gaussian states via the positive partial…
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the…
A hierarchy of multimode uncertainty relations on the second moments of n pairs of canonical operators is derived in terms of quantities invariant under linear canonical (i.e. symplectic) transformations. Conditions for the separability of…
Continuous-variable Gaussian entanglement is an attractive notion, both as a fundamental concept in quantum information theory, based on the well-established Gaussian formalism for phase-space variables, and as a practical resource in…
Following previous work, we distinguish between genuine $N$-partite entanglement and full $N$-partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous variable (position and…
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global…
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in…
Genuine entanglement identification of large scale systems is crucial for quantum computation, quantum communication and quantum learning advantage. In contrast to experiments, where noisy intermediate-scale programmable photonic quantum…
This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All…
A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and…
We demonstrate how to efficiently derive a broad class of inequalities for entanglement detection in multi-mode continuous variable systems. The separability conditions are established from partial transposition (PT) in combination with…
We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The $k$-th condition involves comparing moments of the partially transposed density operator up to order $k$. Remarkably, the…
We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be…
We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical sufficient criterion for detecting…
The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of…
Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. {\bf 95}, 230502 (2005)].…
We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in…