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arXiv:1308.6441 · Physical Review A

Optimized state-independent entanglement detection based on a geometrical threshold criterion

Wiesław Laskowski, Christian Schwemmer, Daniel Richart, Lukas Knips, Tomasz Paterek, Harald Weinfurter

Published Aug 21, 2013• 9 citations
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Abstract

Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation complementarity. Our first scheme essentially establishes the Schmidt decomposition for pure states, with few measurements only and without the need for shared reference frames. The second scheme employs a decision tree to speed up entanglement detection. We analyze the performance of the methods using numerical simulations and verify them experimentally for various states of two, three, and four qubits.

DOI
10.1103/physreva.88.022327

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Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation complementarity. Our first scheme essentially establishes the Schmidt decomposition for pure states, with few measurements only and without the need for shared reference frames. The second scheme employs a decision tree to speed up entanglement detection. We analyze the performance of the methods using numerical simulations and verify them experimentally for various states of two, three, and four qubits.
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The state overlap, quantified via $\tr[ρσ]$, is a metric widely used to assess the closeness between two quantum states ρρρ and σσσ. Although global state overlap alone does not directly capture entanglement properties, we uncover that incorporating local state overlaps provide profound insights into the entanglement characteristics of quantum states. To be precise, the ratio of global to local state overlaps provides a lower bound on the Schmidt number, which is usually used for quantifying high-dimensional entanglement. Unlike conventional methods for detecting entanglement, the approach here can simultaneously reveal entanglement information for two unknown quantum states. Moreover, state overlap can be efficiently determined through local randomized measurement methods, which ensures the experimental feasibility of our approach. In a special case, our criterion reduces to an entanglement criterion that is more powerful than the two criteria used most in experiment--the purity criterion and the fidelity-based criterion and also outperform the p3p_3p3​-PPT method in specific instances. Our findings highlight a promising direction for advancements in entanglement detection experiments.
Constructing optimal entanglement witnesses for arbitrary quantum systems remains a formidable challenge, hindered by the structural complexity of high-dimensional quantum state spaces. In this work, we overcome this barrier by introducing a unified framework for constructing geometrically optimal witnesses capable of identifying arbitrary entanglement structures. By leveraging the geometric properties of a target quantum state relative to a specific entanglement structure in Hilbert-Schmidt space, these witnesses are constructed in an efficient and effective manner. Among all nontrivial witnesses, they provide maximal distinguishability between the target state and the set of states without the desired entanglement structure. As a result, our approach enables the universal detection of bipartite, multipartite, and high-dimensional entanglement. To demonstrate its experimental feasibility, we apply the framework to a four-qubit nuclear spin quantum system. Compared to existing methods, our approach offers enhanced noise robustness, broader detection universality, and improved construction efficiency, providing a powerful and versatile tool for advancing the characterization and understanding of entanglement in quantum systems.
Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.