Experimental detection of entanglement polytopes via local filters

Abstract

Quantum entanglement, resulting in correlations between subsystems that are stronger than any possible classical correlation, is one of the mysteries of quantum mechanics. Entanglement cannot be increased by any local operation, and for a sufficiently large many-body quantum system there exist infinitely many different entanglement classes, i.e., states that are not related by stochastic local operations and classical communications. On the other hand, the method of entanglement polytopes results in finitely many coarse-grained types of entanglement that can be detected by only measuring single-particle spectra. We find, however, that with high probability the local spectra lie in more than one polytope, hence providing only partial information about the entanglement type. To overcome this problem, we propose to additionally use so-called local filters, which are non-unitary local operations. We experimentally demonstrate the detection of entanglement polytopes in a four-qubit system. Using local filters we can distinguish the entanglement type of states with the same single particle spectra, but which belong to different polytopes.

Entanglement of Three-Qubit Random Pure States

“…For such a case the joint probability distribution is known [47] and hence the fraction of random states in the GHZ pyramid was computed in Ref. [50] yielding 13/216 ≈ 6.02% which is consistent with our numerical calculation.…”

“…An equivalent approach can be done dealing with the maximum eigenvalues of the reduced single qubit density matrices. For such a case, the joint probability distribution is known [ 49 ] and hence the fraction of random states in the GHZ pyramid was computed in Reference [ 50 ] yielding which is consistent with our numerical calculation.…”

Testing a Quantum Error-Correcting Code on Various Platforms

“…2 (a), for the optical platform we use an interferometer to implement the detected amplitude damping channel 35 . After passing through the first beam displacer (BD), the photons with horizontal polarization (H) and vertical polarization (V ) are parallelly displaced with respect to each other 36,37 . For the operator A 0 , the amount of damping γ is adjusted by rotating HWP1 placed between two BDs by the angle θ, with sin 2 2θ = 1 − γ.…”

Asymptotic properties of entanglement polytopes for large number of qubits

“…This is done by following the gradient flow of E. The gradient gradE(ψ) is always tangent to C φ at point φ [14], hence the lines of gradient flow can be realised by SLOCC operations. A similar protocol using random SLOCC operations has been realised experimentally in [37]. The main idea behind using the entanglement distillation protocols is the fact that for small systems the critical spectra λ C usually belong to the intersection of a small number of polytopes.…”