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

Characterization of errors in quantum processes using finite sets of test measurements

Holger Friedrich Hofmann

Published Aug 31, 2006• 0 citations
Publisher

Abstract

Quantum information processes utilize the potential of quantum coherence to achieve improvements in communication and computation protocols. In order to develop appropriate technologies, it is therefore necessary to test the successful implementation of quantum coherent operations in experimental devices. In this presentation, it is shown how the quantum coherent performance of a device can be evaluated from complementary test measurements. Despite the limitation of test measurements to only two orthogonal basis sets of states, this method provides a surprisingly detailed and intuitively accessible picture of errors in quantum operations, making it possible to assess the quantum parallelism of non-classical operations in terms of the directly observable "classical" device properties.

DOI
10.1117/12.678878

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Quantum information processes utilize the potential of quantum coherence to achieve improvements in communication and computation protocols. In order to develop appropriate technologies, it is therefore necessary to test the successful implementation of quantum coherent operations in experimental devices. In this presentation, it is shown how the quantum coherent performance of a device can be evaluated from complementary test measurements. Despite the limitation of test measurements to only two orthogonal basis sets of states, this method provides a surprisingly detailed and intuitively accessible picture of errors in quantum operations, making it possible to assess the quantum parallelism of non-classical operations in terms of the directly observable "classical" device properties.
Quantum logic gates can perform calculations much more efficiently than their classical counterparts. However, the level of control needed to obtain a reliable quantum operation is correspondingly higher. In order to evaluate the performance of experimental quantum gates, it is therefore necessary to identify the essential features that indicate quantum coherent operation. In this paper, we show that an efficient characterization of an experimental device can be obtained by investigating the classical logic operations on a pair of complementary basis sets. It is then possible to obtain reliable predictions about the quantum coherent operations of the gate such as entanglement generation and Bell state discrimination even without performing these operations directly.
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, i.e. classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.
It is shown that a quantum controlled-NOT gate simultaneously performs the logical functions of three distinct conditional local operations. Each of these local operations can be verified by measuring a corresponding truth table of four local inputs and four local outputs. The quantum parallelism of the gate can then be observed directly in a set of three simple experimental tests, each of which has a clear intuitive interpretation in terms of classical logical operations. Specifically, quantum parallelism is achieved if the average fidelity of the three classical operations exceeds 2∕32∕32∕3. It is thus possible to evaluate the essential quantum parallelism of an experimental controlled-NOT gate by testing only three characteristic classical operations performed by the gate.
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2)O(d^2)O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g. certifying non-classicality in quantum communication and simulation protocols and probing the quantum behaviour of biological complexes.