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arXiv:1212.5046 · New Journal of Physics

Complementarity reveals bound entanglement of two twisted photons

Beatrix C. Hiesmayr, W. Löffler

Published Aug 20, 2013• 40 citations
arXivHTMLPDF

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.

DOI
10.1088/1367-2630/15/8/083036

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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.
Entanglement detection in high-dimensional quantum systems, such as of photons entangled in their orbital angular momentum degree of freedom, is complex. We present a simple protocol that is only based on complementarity to detect such high-dimensional entanglement, and demonstrate it experimentally by observing 2-photon bound entanglement of OAM-entangled photons. This particular type of entanglement is interesting because no pure entanglement can be obtained via entanglement distillation; and most methods for entanglement detection fail. We analyze the twin photons by state tomography and direct measurement of the probabilities and find excellent agreement with theory.
Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find [Formula: see text] to be free entangled, [Formula: see text] to be certainly separable and as much as [Formula: see text] to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining [Formula: see text] of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.
Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.
We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing.
Bound entanglement is a special form of quantum entanglement that cannot be used for distillation, i.e. the local transformation of copies of arbitrarily entangled states into a smaller number of approximately maximally entangled states. Implying an inherent irreversibility of quantum resources, this phenomenon highlights the gaps in our current theory of entanglement. This review provides a comprehensive exploration of the key findings on bipartite bound entanglement. We focus on systems of finite dimensions, an area of high relevance for many quantum information processing tasks. We elucidate the properties of bound entanglement and its interconnections with various facets of quantum information theory and quantum information processing. The paper highlights areas where our understanding of bound entangled states, particularly in their detection and characterization, remains underdeveloped. By highlighting the need for further research into this phenomenon and underscoring relevant open questions, this paper invites researchers to unravel its relevance for our understanding of entanglement in Nature and how this resource can most effectively be used for applications in quantum technology.
Photon pairs generated from spontaneous parametric down-conversion are a well-established method to realize entangled bipartite photonic systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly exploited to engineer high-dimensional entangled quantum states. For Hilbert spaces with dimension d>2d>2d>2, maximally entangled states (MESs) help to improve the capacity and security of quantum communication protocols, among several other promising features. However, the direct generation of MESs in well-defined high-dimensional subspaces of the infinite OAM basis has remained a challenge. Here, we formalize how the spatial distribution of the pump beam and the nonlinear profile of the crystal can be simultaneously utilized to generate MESs without additional spatial filtering of OAM modes within a subspace. We illustrate our approach with maximally entangled qutrits (d=3)(d=3)(d=3) and ququints (d=5)(d=5)(d=5).