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Register a new userA Witness of Multipartite Entanglement Strata
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Added by
Dagomir Kaszlikowski
Publication date
2008
fields
Physics
and research's language is
English
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We describe an entanglement witness for $N$-qubit mixed states based on the properties of $N$-point correlation functions. Depending on the degree of violation, this witness can guarantee that no more than $M$ qubits are separable from the rest of the state for any $Mleq N$, or that there is some genuine $M$-party or greater multipartite entanglement present. We illustrate the use our criterion by investigating the existence of entanglement in thermal stabilizer states, where we demonstrate that the witness is capable of witnessing bound-entangled states. Intriguingly, this entanglement can be shown to persist in the thermodynamic limit at arbitrary temperature.
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We derive energy minima for biseparable states in three- and four-spin systems, with Heisenberg Hamiltonian and s <= 5/2. These provide lower bounds for tripartite and quadripartite entanglement in chains and rings with larger spin number N. We demonstrate that the ground state of an $N$-spin Heisenberg chain is $N$-partite entangled, and compute the energy gap with respect to biseparable states for N <= 8.
Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearest-neighbour two-mode marginals. The key tool of our construction is a genuine multipartite entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semi-definite programme. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.
We introduce a feasible method of constructing the entanglement witness that detects the genuine entanglement of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are broadly theoretically and experimentally investigated. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.
Any bipartite entanglement witness $W$ can be written as $W=c_{sigma}I-sigma$, where $sigma$ is a quantum state, $I$ is the identity matrix, and $c_{sigma}$ is a non-negative number. We present a general method to extend the given entanglement witness to multipartite cases via purification, partial purification, and direct tensor of the quantum state $sigma$. Our methods extend $sigma$ but leave the parameter $c_{sigma}$ untouched. This is very valuable since the parameter is generally not easy to compute.
Hybrid encoding of quantum information is a promising approach towards the realisation of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable ressource for quantum information protocols. In this work, we present a hybrid entanglement witness that can be implemented on currently available experiments and is robust to noise currently observed in quantum optical set-ups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterised with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables.
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