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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Benchmarking and procrustean noise reduction of entangled mixed states

Nicholas A. Peters, Tzu-Chieh Wei, Paul G. Kwiat

Published May 25, 2004• 2 citations

Abstract

Understanding quantum noise is essential for accurately creating desired quantum states and for examining a given state's evolution in any protocol. Using spontaneous parametric downconversion, we can create a wide variety of single- and two-qubit polarization states, including nearly perfect Bell states, mixed states (i.e., "noisy" states) and maximally entangled mixed states (MEMS). To characterize these states we use several different measures, including fidelity, "tangle" and linear entropy. In the course of our experiments, we have discovered and numerically investigated an extreme imbalance in the sensitivity of these different two-qubit state measures. We have also experimentally realized a "Procrustean" filtering technique to remove noise from MEMS. For moderate amounts of filtering, the experimental procedure works as desired to increase the tangle and decrease the linear entropy. However, for large amounts of filtering, the process becomes dominated by perturbations in the starting density matrix. The final outcome is a pure (i.e., zero entropy) product state (i.e., zero entanglement).

DOI: 10.1117/12.546857

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Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.

Using a spontaneous parametric-downconversion source of photon pairs, we are working towards the creation of arbitrary 2-qubit quantum states with high fidelity. Currently, all physically allowable combinations of polarization entanglement and mixture can be produced, including maximally-entangled mixed states. The states are experimentally measured and refined via computer-automated quantum-state tomography, and this system has also been used to perform single-qubit and ancilla-assisted quantum process tomography.

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The idea of exploiting maximally entangled states as a resource lies at the core of several modalities of quantum information processing, including secure quantum communication, quantum computation, and quantum sensing. However, due to imperfections during or after the entangling gates used to prepare such states, the amount of entanglement decreases and their quality as a resource gets degraded. We introduce a low-overhead protocol to reverse this degradation by partially filtering out a specific type of noise relevant to many quantum technologies. We present two trapped-ion schemes for the implementation of a nonunitary probabilistic filter against amplitude damping noise, which can protect any maximally entangled pair from spontaneous photon scattering during or after the two-qubit trapped-ion entangling gates. This filter can be understood as a protocol for single-copy quasidistillation, as it uses only local operations to realize a reversal operation that can be understood in terms of weak measurements.