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arXiv:0808.0776

Experimental Measurement of Lower and Upper Bounds of Concurrence for Mixed Quantum States

Xiao-Ling Niu, Yan-Xiao Gong, Jian Li, Peng, Liang, Chengjie Zhang, Yongsheng Zhang, Yun‐Feng Huang, Guang‐Can Guo

Published Aug 6, 2008• 0 citations
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Abstract

We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructed through quantum state tomography. In our experiment, we propose and demonstrate a simple method to provide two faithful copies of a two-photon mixed state required for parity measurements: Two photon pairs generated by two neighboring pump laser pulses through optical parametric down conversion processes represent two identical copies. This method can be conveniently generalized for entanglement estimation of multi-photon mixed states.

DOI
10.48550/arxiv.0808.0776

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We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructed through quantum state tomography. In our experiment, we propose and demonstrate a simple method for providing two faithful copies of a two-photon mixed state required for parity measurements: two photon pairs generated by two neighboring pump-laser pulses through optical parametric down-conversion processes represent two identical copies. This method can be conveniently generalized for entanglement estimation of multiphoton mixed states.
We report on the direct estimation of concurrence for mixed quantum states. The used method relies on joint measurements on two copies of an entangled state. In the experimental demonstration two polarization-entangled photon pairs emitted from spontaneous parametric down-conversion are analyzed together using a linear optics controlled phase gate. We demonstrate that the measured data, without need for further numerical processing, directly yield reliable estimates, despite experimental imperfections.
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Two-photon entangled quantum states are a fundamental tool for quantum information and quantum cryptography. A complete description of a generic quantum state is provided by its density matrix: the technique allowing experimental reconstruction of the density matrix is called quantum state tomography. Entangled states density matrix reconstruction requires a large number of measurements on many identical copies of the quantum state. An alternative way of certifying the amount of entanglement in two-photon states is represented by the estimation of specific parameters, e.g., negativity and concurrence. If we have a priori partial knowledge of our state, it's possible to develop several estimators for these parameters that require lower amount of measurements with respect to full density matrix reconstruction. The aim of this work is to introduce and test different estimators for negativity and concurrence for a specific class of two-photon states.
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 construct a linear optics measurement process to determine the entanglement measure, named III concurrence, of a set of $4\ifmmode\times\else\texttimes\fi{}4$-dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an equivalent symmetric projection for the twofold copy of a single subsystem [presented by L. Aolita and F. Mintert, Phys. Rev. Lett. 97, 050501 (2006)] can be realized by observing the one-side two-photon coincidence without any triggering detection on the other subsystem. Here, for the first time, we realize the measurement for entanglement contained in biphoton pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the III concurrence of generic high-dimensional bipartite pure states produced in the parametric down conversion process.