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arXiv:1302.0205 · Physical Review A

Quantum probes to experimentally assess correlations in a composite system

Andrea Smirne, S. Cialdi, Giorgio Anelli, Matteo G. A. Paris, Bassano Vacchini

Published Jul 11, 2013• 33 citations
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Abstract

We suggest and demonstrate a technique to obtain relevant information about a composite system by performing measurements on only a small and easily accessible part of it, which we call a quantum probe. We show in particular how quantitative information about the angular correlations of pairs of entangled photons generated by spontaneous parametric down-conversion may be accessed through the study of the trace distance between two polarization states evolved from different initial conditions. After estimating the optimal polarization states to be used as the quantum probe, we provide a detailed analysis of the connections between the increase of the trace distance above its initial value and the amount of angular correlation.

DOI
10.1103/physreva.88.012108

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We suggest and demonstrate a technique to obtain relevant information about a composite system by performing measurements on only a small and easily accessible part of it, which we call a quantum probe. We show in particular how quantitative information about the angular correlations of pairs of entangled photons generated by spontaneous parametric down-conversion may be accessed through the study of the trace distance between two polarization states evolved from different initial conditions. After estimating the optimal polarization states to be used as the quantum probe, we provide a detailed analysis of the connections between the increase of the trace distance above its initial value and the amount of angular correlation.
The trace distance between two states of an open quantum system quantifies their distinguishability and, for a fixed environmental state, can increase above its initial value only in the presence of initial system-environment correlations. We provide experimental evidence of such a behavior. In our all-optical apparatus, we exploit spontaneous parametric down conversion as a source of polarization entangled states and a spatial light modulator to introduce in a general fashion correlations between the polarization and the momentum degrees of freedom, which act as environment.
This paper presents a method to convert position correlation of photon pairs into polarization entanglement. This is achieved by individually manipulating the polarization state of photons generated in different parts of a nonlinear medium and coherently superposing them. This concept is experimentally demonstrated using photon pairs produced by spontaneous parametric down-conversion. The method is used to implement a compact source producing an observed photon-pair rate of $120\phantom{\rule{0.16em}{0ex}}000\phantom{\rule{4.pt}{0ex}}{\text{s}}^{\ensuremath{-}1}/\text{mW}$ with an entanglement fidelity of $0.991\ifmmode\pm\else\textpm\fi{}0.013$. This method can be extended to any photon-pair generation process with initial position correlation.
Developing techniques for characterizing quantum mechanical systems has been a major topic of research, especially in recent years, as quantum technologies, such as quantum communication and quantum cryptography, have grown to become an important asset in modern society. Although techniques such as quantum state tomography is an effective method to characterize a system consisting of two-level systems, the characterization of continuous degree of freedom such as space or frequency stills represents a time-consuming task as the state space scales exponentially with the dimension of the system. In this work, we show an indirect approach for measuring properties of high-dimensional degrees of freedom by coupling them to two-dimensional subsystems that can be measured efficiently via quantum state tomography. In our case, the property of interest is the correlation factor of the joint spectral amplitude describing the two-photon frequency states, which are coupled to the polarization degree of freedom using a completely positive trace-preserving map, called a dephasing channel. The action of the map on the polarization state induces a decoherence effect that depends on the initial frequency state, thus allowing to retrieve information about the frequency correlation factor by only measuring the decoherence in the polarization state. In the experimental part, we produced a pair of photons using spontaneous parametric down-conversion and characterized the joint spectral intensity with stimulated emission tomography. The decoherence was controlled with a birefringent material that acts as a dephasing channel. The polarization state was measured after the dephasing channel for two different initial frequency configurations using quantum state tomography. The bounds for the frequency correlation factor were calculated from the fidelity of the two polarization states and the generalized data processing inequality. The results of this work show that the polarization decoherence can be used as a tool to measure the frequency correlation factor of the joint spectral amplitude.
We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to precision. In particular, we present a set of experiments aimed at measuring the amount of entanglement for states belonging to different families of pure and mixed two-qubit two-photon states. Our scheme is based on visibility measurements of quantum correlations and achieves the ultimate precision allowed by quantum mechanics in the limit of Poissonian distribution of coincidence counts. Although optimal estimation of entanglement does not require the full tomography of the states we have also performed state reconstruction using two different sets of tomographic projectors and explicitly shown that they provide a less precise determination of entanglement. The use of optimal estimators also allows us to compare and statistically assess the different noise models used to describe decoherence effects occurring in the generation of entanglement.
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply rooted, yet rarely discussed question of why quantum states are described via complex numbers. With our experiment, we then realize two-photon polarization states that are entangled with respect to the notion of two rebits, comprising two two-level systems over real numbers. At the same time, the generated states are separable with respect to two complex qubits. Among other results, we reconstruct the best approximation of the generated states in terms of a real-valued, local expansion and show that this yields an incomplete description of our data. Conversely, the generated states are shown to be fully decomposable in terms of tensor-product states with complex wave functions. Thereby, we probe paradigms of quantum physics with modern theoretical tools and experimental platforms that are relevant for applications in quantum information science and technology and connected to the fundamentals of the quantum description of nature.
In any natural science, measurements are the essential link between theory and observable reality. Is it possible to obtain accurate and relevant information via measurement whose action on the probed system is unknown? In other words, can one be convinced to know something about the nature without knowing in detail how the information was obtained? In this paper, we show that the answer is, surprisingly, yes. We construct and experimentally implement a quantum optical probing measurement where measurements on the probes, i.e., the photons' polarization states, are used to extract information on the systems, i.e., the frequency spectra of the same photons. Unlike the preexisting probing protocols, our measurement does not require any knowledge of the interaction between the probe and the system.