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Physical Review A

Experimental realization of dimension witnesses based on quantum state discrimination

Yong-Nan Sun, Zhao‐Di Liu, Jun Ying Sun, Geng Chen, Xiao‐Ye Xu, Yu-Chun Wu, Jian‐Shun Tang, Yong‐Jian Han, Chuan‐Feng Li, Guang‐Can Guo

Published Nov 10, 2016• 7 citations
Publisher

Abstract

The dimension witness is an important concept in fundamental physics and quantum information processing which allows one to test the dimension of an unknown physical system in a device independent manner. Here, we report an experimental test of classical and quantum dimensions in a prepare and measure scenario through dimension witnesses based on quantum state discrimination. In our work, we have not only distinguished between quantum and classical systems of the same dimension (two, three, and four dimensions) but also distinguished between real and complex two-level quantum systems. We have also shown the strong link between dimension witnesses and quantum state discrimination which was introduced in N. Brunner, M. Navascu\'es, and T. V\'ertesi [Phys. Rev. Lett. 110, 150501 (2013)].

DOI
10.1103/physreva.94.052313

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The dimension witness is an important concept in fundamental physics and quantum information processing which allows one to test the dimension of an unknown physical system in a device independent manner. Here, we report an experimental test of classical and quantum dimensions in a prepare and measure scenario through dimension witnesses based on quantum state discrimination. In our work, we have not only distinguished between quantum and classical systems of the same dimension (two, three, and four dimensions) but also distinguished between real and complex two-level quantum systems. We have also shown the strong link between dimension witnesses and quantum state discrimination which was introduced in N. Brunner, M. Navascu'es, and T. V'ertesi [Phys. Rev. Lett. 110, 150501 (2013)].
Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.
We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semi-device-independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.
In quantum information processing, it is important to witness the entropy of the message in the device-independent way which was proposed recently [R. Chaves, J. B. Brask, and N. Brunner, Phys. Rev. Lett. 115, 110501 (2015)]. In this paper, we theoretically obtain the minimal quantum entropy for three widely used linear dimension witnesses, which is considered ``a difficult question.'' Then we experimentally test the classical and quantum entropy in a device-independent manner. The experimental results agree well with the theoretical analysis, demonstrating that entropy is needed in quantum systems that is lower than the entropy needed in classical systems with the given value of the dimension witness.
Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this problem in the prepare-and-measure scenario. Specifically, we provide a lower bound on the dimension of the prepared quantum systems, which is a function that only depends on the measurement statistics. Furthermore, we show that our bound performs well in several examples. In particular, we show that our bound provides insights into the notion of dimension witness, and we also use it to show that the sets of restricted-dimensional prepare-and-measure correlations are not always convex.
Device-independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a ``black box''scenario where only correlations between preparations, measurements, and outcomes are considered. We address the problem of the robustness of dimension witnesses, namely that to witness the dimension of a system or to discriminate between its quantum or classical nature, even in the presence of loss. We consider the case when shared randomness is allowed between preparations and measurements and provide a threshold in the detection efficiency such that dimension witnessing can still be performed.
Dimensionality plays an important role in various information-theoretic tasks and can be seen as a key resource for quantum information processing. In this work, for the first time to the best of our knowledge, we report an experimental test of classical and quantum dimensions in a prepare-and-measure scenario through a nonlinear dimension witness (NDW), where the preparer and the measurer have no shared randomness. We propose a theoretical method to certify whether the generated states can be decomposed as products of lower dimensional states with the NDW, certify the dimension of the high-dimensional system, and identify whether the quantum system is irreducible in a unified picture in our experiment. To demonstrate the practicability of this method, we experimentally witness the generation of classical and quantum systems encoded in the high-dimensional orbital angular momentum (OAM) state under the effects of atmospheric turbulence. Our results show that this nonlinear dimension witness is highly robust and can be used in the presence of noise and low detection efficiency; hence, we estimate the dimension in our experiment in a detection-loophole-free manner through the NDW. We believe our work opens new avenues for dimension witnesses, especially for device-independent estimation of quantum systems and quantum communications.