Abstract
Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of3×3and4×4systems, and find that the experimental certification of bound entangled states is well within reach.
Highlights
To experimentally prepare, characterize and control entangled quantum states is an essential item in the development of quantum-enhanced technologies, but it serves the indispensable purpose of testing the predictions of entanglement theory in the laboratory
Considered as useless for quantum information processing, bound entangled states were later established as a valid resource in the contexts of quantum key distribution [2], entanglement activation [3, 4], metrology [5, 6], steering [7], and nonlocality [8], and their nondistillability has been linked to irreversibility in thermodynamics [9, 10]
Instead of advocating for a particular tomographic method for detecting bound entanglement or considering the preparation of a specific state, we address the more generic question: Which are the best candidate states for an experimental verification of bound entanglement? In other words, for bipartite systems, we aim at finding states that have the largest ball of bound entangled states around them [35]
Summary
Characterize and control entangled quantum states is an essential item in the development of quantum-enhanced technologies, but it serves the indispensable purpose of testing the predictions of entanglement theory in the laboratory. There exist more informative methods to derive errors from tomographic data, such as credibility [29] and confidence [30, 31] regions, and the alternative of using linear inversion in addition to a sufficiently large number of measurements that guarantees physical estimates [32] Should these methods be applied to the detection of a bound entangled state, more robust results may be generated, they might come at the expense of being computationally expensive or even intractable [33]. At least for the known cases in lowdimensional systems, bound entangled states are close to both the sets of separable states and distillable entangled states This translates into the requirement of a highly precise experimental setup, and the deepening of the potential pitfalls of biased tomographic reconstructions. We proceed to devise a hypothesis test for bound entanglement, and test the robustness of the selected candidate states in terms of the necessary number of samples to achieve a statistically significant certification under realistic experimental conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
