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Solvay Conference on Physics

DIRECT DETECTION OF QUANTUM ENTANGLEMENT

Paweł Horodecki, ARTUR K. EKERT, CAROLINA MOURA ALVES, Daniel K. L. Oi, L. C. Kwek, Dagomir Kaszlikowski, Michał Horodecki

Published Aug 1, 2003• 11 citations
Publisher

Abstract

Quantum entanglement, after playing a significant role in the development of the foundations of quantum mechanics, has been recently rediscovered as a new physical resource with potential commercial applications such as, for example, quantum cryptography, better frequency standards or quantum-enhanced positioning and clock synchronization. On the mathematical side the studies of entanglement have revealed very interesting connections with the theory of positive maps. The capacity to generate entangled states is one of the basic requirements for building quantum computers. Hence, efficient experimental methods for detection, verification and estimation of quantum entanglement are of great practical importance. Here, we propose an experimentally viable, \\emph{direct} detection of quantum entanglement which is efficient and does not require any \\emph{a priori} knowledge about the quantum state. In a particular case of two entangled qubits it provides an estimation of the amount of entanglement. We view this method as a new form of quantum computation, namely, as a decision problem with quantum data structure.

DOI
10.1142/9789812704634_0043

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Quantum entanglement, after playing a significant role in the development of the foundations of quantum mechanics, has been recently rediscovered as a new physical resource with potential commercial applications such as, for example, quantum cryptography, better frequency standards or quantum-enhanced positioning and clock synchronization. On the mathematical side the studies of entanglement have revealed very interesting connections with the theory of positive maps. The capacity to generate entangled states is one of the basic requirements for building quantum computers. Hence, efficient experimental methods for detection, verification and estimation of quantum entanglement are of great practical importance. Here, we propose an experimentally viable, \emph{direct} detection of quantum entanglement which is efficient and does not require any \emph{a priori} knowledge about the quantum state. In a particular case of two entangled qubits it provides an estimation of the amount of entanglement. We view this method as a new form of quantum computation, namely, as a decision problem with quantum data structure.
Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates keeps being a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of parties or require more information on the state than what is attainable in every-day experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, its scales efficiently with the number of parties, thus allowing for application to systems composed by up to few tens of parties. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device-independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.
Since the 1980s, there has been a physical problem relating to the detection of multipartite entangled states that helps us to investigate fundamental point of view on interpretations of quantum mechanics. On the other hand, information theories based on the mathematical structure of quantum mechanics, for example, quantum cryptography and quantum computation, have been investigated by researchers whose number has been increasing day by day in the world. This field became to be called quantum information theories. A practical experimental realization of quantum information processing needs that we detect experimentally multipartite entangled states. The number of researchers for multipartite entangled states is increasing rapidly. Especially, Greenberger-Horne-Zeilinger (GHZ) states are useful for quantum information processing information processing using quantum mechanics, which improves the conventional information processing ability which had been based on classical theories. However, practical experimental realization of the theories and controlling quantum states have inevitable difficulties due to the interaction with environments. The requirement in maintaining multipartite entangled states in relation to the time that takes to make a practical experiment is also a problem. Many experimentalists are tackling this problem, and recently, several groups have reported that multipartite entangled states have been physically detected in their laboratories. The main difficulty is how to judge whether or not the observed quantum state is indeed a multipartite entangled state. For this purpose, it is necessary to construct theoretical models to analyze such experimental data. In this thesis, we apply a mathematical structure as to density operators described in a high-dimensional Hilbert space, and we employ mathematical theories to prove if the corresponding density operator represents a multipartite entangled state or not. The main aim for constructing such models is to analyze the raw experimental data. Moreover, this model helps experimentalists in the sense that it allows them to see how to confirm that observed states are indeed the desired state. With mathematical theories developed before this thesis, only limited applications for this purpose were allowed. Some theories cover two-dimensional Hilbert space only. It has not been even discussed how to analyze the fidelity to GHZ states of the observed state. This has led to some doubt of that experimental data might not always confirm three-partite entangled states. However, by using the method of this thesis, statistical check based on such experimental data of the existence of three particle-entangled states is possible under appropriate assumptions. This example symbolizes that our analytical knowledge has improved very much in the last few years. This thesis gives us an advanced mathematical model for analyzing experimental data.
Abstract. Quantum computation, in particular Grover’s algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an N element database require at most O(N) time complexity. Grover’s algorithm is able to find a solution with high prob-ability in O( N) time through an amplitude amplification scheme. In this work we draw elements from both classical and quantum computation to develop an alternative search proposal based on quantum entanglement detection schemes. In 2002, Horodecki and Ekert proposed an efficient method for direct detection of quantum entanglement. Our proposition to quantum search combines quantum entanglement detection along-side entanglement inducing operators. Grover’s quantum search relies on measuring a quantum superposition after having applied a unitary evolution. We deviate from the standard method by focusing on fine-tuning a unitary operator in order to infer the solution with certainty. Our proposal sacrifices space for speed and depends on the mathematical properties of linear positive maps Λ which have not been operationally characterized. Whether such a Λ can be easily determined remains an open question.
Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum entanglement, which allows for quantum computations outperforming their classical counterparts. However, the task of entanglement detection is not always straightforward for several reasons. One of the main challenges is that standardly-used methods rapidly become unfeasible when dealing with quantum states containing more than a few qubits. Typically, this is due to the fact that a vast amount of measurements is needed on many copies of the state. Generally, it is not unusual to deal with a very limited number of state copies in experimental settings - in fact, this may be the case for many large quantum systems. In this article, an overview is provided of a probabilistic approach that enables high-confidence genuine multipartite entanglement detection using an exceptionally low number of state copies. Additionally, a study is presented that shows that this protocol remains efficient also in the presence of noise, thus confirming the practicality of the method for near-term quantum devices and its suitability for complex experimental settings.