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Entropy

Experimentally Demonstrate the Spin-1 Information Entropic Inequality Based on Simulated Photonic Qutrit States

Lianzhen Cao, Xia Liu, Yang Yang, Qinwei Zhang, Jia-Qiang Zhao, Huai-Xin Lu

Published Feb 15, 2020• 0 citations
Publisher

Abstract

Quantum correlations of higher-dimensional systems are an important content of quantum information theory and quantum information application. The quantification of quantum correlation of high-dimensional quantum systems is crucial, but difficult. In this paper, using the second-order nonlinear optical effect and multiphoton interference enhancement effect, we experimentally implement the photonic qutrit states and demonstrate the spin-1 information entropic inequality for the first time to quantitative quantum correlation. Our work shows that information entropy is an important way to quantify quantum correlation and quantum information processing.

DOI
10.3390/e22020219

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Quantum correlations of higher-dimensional systems are an important content of quantum information theory and quantum information application. The quantification of quantum correlation of high-dimensional quantum systems is crucial, but difficult. In this paper, using the second-order nonlinear optical effect and multiphoton interference enhancement effect, we experimentally implement the photonic qutrit states and demonstrate the spin-1 information entropic inequality for the first time to quantitative quantum correlation. Our work shows that information entropy is an important way to quantify quantum correlation and quantum information processing.
Inequalities of information entropic play a fundamental role in information theory and have been employed effectively in finding bounds on optimal rates of various information-processing tasks. In this paper, we perform the first experimental demonstration of the information-theoretic spin-1/2 inequality using the high-fidelity entangled state. Furthermore, we study the evolution of information difference of entropy when photons passing through different noisy channels and give the experimental rules of the information difference degradation. Our work provides an new essential tool for quantum information processing and measurement, and offers new insights into the dynamics of quantum correlation in open systems.
Higher dimensional quantum systems have a very important role to play in quantum information, computation as well as communication. In photonic systems, it is common to use the photon's polarization degree of freedom for various investigations. However, this restricts us to only two orthogonal states, hence qubits for manipulation. In this paper, we have theoretically analysed and experimentally demonstrated a system of two photonic qutrits which are correlated in the spatial degree of freedom. The qutrits have been generated by modulating the pump beam in a spontaneous parametric down conversion process using an aperture based system. In principle, this system can be scaled up to generation of even higher dimensional correlated qudits with possible application for quantum communication and computation implementations.
The nonadditivity of channel capacity is a defining feature that distinguishes quantum communication from classical communication. In the quantum realm, the channel capacity is determined by coherent information, which is defined through the von Neumann entropies of the output and its environment. Despite its fundamental importance, experimental evidence of such nonadditive quantum communication has been elusive because of the complexity of the required quantum channel. Here, we experimentally observe entropic-singularity-induced coherent-information nonadditivity using the qutrit platypus channel implemented on a photonic platform. By preparing six-dimensional photonic entanglement, we directly measure the coherent information of a platypus channel, a qubit amplitude damping channel, and their joint uses, revealing a clear violation of additivity. Quantum process tomography further reveals the entropic singularity responsible for this effect, demonstrating how singular entropy landscapes in low-dimensional channels can enhance quantum communication beyond additive limits.
Higher dimensional quantum systems are an important avenue for new explorations in quantum computing as well as quantum communications. One of the ubiquitous resources in quantum technologies is entanglement. However, so far, entanglement has been certified in higher dimensional systems through suitable bounds on known entanglement measures. In this work, we have, for the first time, quantified the amount of entanglement in bi-partite pure qutrit states by analytically relating statistical correlation measures and known measures of entanglement, and have determined the amount of entanglement in our experimentally generated spatially correlated bi-partite qutrit system. We obtain the value of Negativity in our bi-partite qutrit to be 0.85 +/- 0.03 and the Entanglement of Formation(EOF) to be 1.23 +/- 0.01. In terms of quantifying the deviation from the maximally entangled state, the Negativity value demonstrates ~15 % deviation while the EOF value demonstrates ~24 % deviation. This serves as the first experimental evidence of such non-equivalence of entanglement measures for higher dimensional systems.
Using the information-theoretic inequality proposed by Braunstein and Caves, we study the evolution of quantum correlation in the presence of different noisy channels. First, we experimentally prepare the high-fidelity two-bit entangled state and simulated the bit-flip and phase-shift noise using an all-optical experimental setup. Then, we study the quantum correlation evolution of a two-bit entangled system using the information difference of entropy under different noisy channels and noisy environments. It is found that the quantum correlation degradation depends on the type of noise and noisy channels. Our work provides a new essential tool for quantum information processing and measurement, and offers new insight into the evolution of quantum correlation in open systems.
The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity condition, and monotonicity of relative entropy for a single qudit corresponding to an arbitrary spin state with spin j are discussed. The idea to employ quantum correlations in the single-qudit state, such as the entanglement, for developing a new quantum technique in quantum computing and quantum communication is proposed. Examples of qutrit and qudit with j = 3/2 are considered.