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Register a new userThe invariant-comb approach and its relation to the balancedness of multipartite entangled states
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The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call {em comb} in reference to the {em hairy-ball theorem}. An appealing feature of this approach is that for qubits (or spins 1/2) the combs are automatically invariant under $SL(2,CC)$, which implies that the obtained invariants are entanglement monotones by construction. By asking which property of a state determines whether or not it is detected by a polynomial $SL(2,CC)$ invariant we find that it is the presence of a {em balanced part} that persists under local unitary transformations. We present a detailed analysis for the maximally entangled states detected by such polynomial invariants, which leads to the concept of {em irreducibly balanced} states. The latter indicates a tight connection with SLOCC classifications of qubit entanglement. Combs may also help to define measures for multipartite entanglement of higher-dimensional subsystems. However, for higher spins there are many independent combs such that it is non-trivial to find an invariant one. By restricting the allowed local operations to rotations of the coordinate system (i.e. again to the $SL(2,CC)$) we manage to define a unique extension of the concurrence to general half-integer spin with an analytic convex-roof expression for mixed states.
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I generalize the concept of balancedness to qudits with arbitrary dimension $d$. It is an extension of the concept of balancedness in New J. Phys. {bf 12}, 075025 (2010) [1]. At first, I define maximally entangled states as being the stochastic states (with local reduced density matrices $id/d$ for a $d$-dimensional local Hilbert space) that are not product states and show that every so-defined maximal genuinely multi-qudit entangled state is balanced. Furthermore, all irreducibly balanced states are genuinely multi-qudit entangled and are locally equivalent with respect to $SL(d)$ transformations (i.e. the local filtering transformations (LFO)) to a maximally entangled state. In particular the concept given here gives the maximal genuinely multi-qudit entangled states for general local Hilbert space dimension $d$. All genuinely multi-qudit entangled states are an element of the partly balanced $SU(d)$-orbits.
An analysis is conducted of the multipartite entanglement for Gaussian states generated by the parametric down-conversion of a femtosecond frequency comb. Using a recently introduced method for constructing optimal entanglement criteria, a family of tests is formulated for mode decompositions that extends beyond the traditional bipartition analyses. A numerical optimization over this family is performed to achieve maximal significance of entanglement verification. For experimentally prepared 4-, 6-, and 10-mode states, full entanglement is certified for all of the 14, 202, and 115974 possible nontrivial partitions, respectively.
In the physics of flavor mixing, the flavor states are given by superpositions of mass eigenstates. By using the occupation number to define a multiqubit space, the flavor states can be interpreted as multipartite mode-entangled states. By exploiting a suitable global measure of entanglement, based on the entropies related to all possible bipartitions of the system, we analyze the correlation properties of such states in the instances of three- and four-flavor mixing. Depending on the mixing parameters, and, in particular, on the values taken by the free phases, responsible for the CP-violation, entanglement concentrates in preferred bipartitions. We quantify in detail the amount and the distribution of entanglement in the physically relevant cases of flavor mixing in quark and neutrino systems. By using the wave packet description for localized particles, we use the global measure of entanglement, suitably adapted for the instance of multipartite mixed states, to analyze the decoherence induced by the free evolution dynamics on the quantum correlations of stationary neutrino beams. We define a decoherence length as the distance associated with the vanishing of the coherent interference effects among massive neutrino states. We investigate the role of the CP-violating phase in the decoherence process.
Recently, Halder emph{et al.} [S. Halder emph{et al.}, Phys. Rev. Lett. textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $2 otimes 2 otimes 2$ quantum system, we show that a set of orthogonal entangled states is locally reducible but locally indistinguishable in all bipartitions, which means the states have strong nonlocality. Furthermore, we generalize the result in N-qubit quantum system, where $Ngeqslant 3$. Finally, we also construct a class of strong nonlocality of entangled states in $dotimes dotimes cdots otimes d, dgeqslant 3$. Our results extend the phenomenon of strong nonlocality for entangled states.
We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.
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