Abstract
We demonstrate the detection of bipartite bound entanglement as predicted by the Horodecki's in 1998. Bound entangled states, being heavily mixed entangled quantum states, can be produced by incoherent addition of pure entangled states. Until 1998 it was thought that such mixing could always be reversed by entanglement distillation; however, this turned out to be impossible for bound entangled states. The purest form of bound entanglement is that of only two particles, which requires higher-dimensional (d > 2) quantum systems. We realize this using photon qutrit (d = 3) pairs produced by spontaneous parametric downconversion, that are entangled in the orbital angular momentum degrees of freedom, which is scalable to high dimensions. Entanglement of the photons is confirmed via a ‘maximum complementarity protocol’. This conceptually simple protocol requires only maximized complementary of measurement bases; we show that it can also detect bound entanglement. We explore the bipartite qutrit space and find that, also experimentally, a significant portion of the entangled states are actually bound entangled.
Highlights
We demonstrate the detection of bipartite bound entanglement as predicted by the Horodecki’s in 1998
We use experimentally photons that are entangled in their orbital angular momentum degrees of freedom to simulate a bound entangled bipartite state, on which we apply the maximum complementarity protocol using sets of complementary observables to directly witness the inseparability
In [47] we have shown via geometry considerations that if a Hermitian operator detects entanglement of states in a certain quantum space W, it detects entanglement in the multi-partite product space W⊗n := {ρd,⊗n = ck,l Pk,l|ck,l
Summary
Consider the following scenario of a source producing two-qudit states ρ ∈ Cd×d, namely quantum states with d degrees of freedom per qudit. We introduce a measurement-based scheme to produce these mixed states similar to the authors in [2,3,4, 42, 43] for polarization, but in our case for OAM qutrits using spatial light modulation, see figure 2 to apply single-qutrit rotations (ROTs) (e.g. on qutrit A) using the Weyl matrix Wk,l to transform P0,0 into any of the eight other maximally entangled Bell states Pk,l This operation is implemented on the spatial light modulators (SLMs, see figure 2), which allows us to generate the mixed state by time-multiplexing of the ROT operators Wk,l for a particular choice of qi. If Bob and Alice are given this experimental data, they cannot reverse the procedure since a test does not exist to distinguish in which way the mixing was done nor in which way the mixed state was created at all
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