Physical Implementation

Giuseppe Gaeta, Miguel A. Rodrı́guez

Jiaqing Jiang, Kun Wang, Xin Wang

Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ingredients in quantum information, both in theoretical and practical perspectives. This raises the question of how well one can simulate or approximate the action of a general linear map by physically implementable operations. In this work, we introduce a systematic framework to resolve this task using the quasiprobability decomposition technique. We decompose a target linear map into a linear combination of physically implementable operations and introduce the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain, which directly quantifies the cost of simulating a given map using physically implementable quantum operations. We show this measure is efficiently computable by semidefinite programs and prove several properties of this measure, such as faithfulness, additivity, and unitary invariance. We derive lower and upper bounds in terms of the Choi operator's trace norm and obtain analytic expressions for several linear maps of practical interests. Furthermore, we endow this measure with an operational meaning within the quantum error mitigation scenario: it establishes the lower bound of the sampling cost achievable via the quasiprobability decomposition technique. In particular, for parallel quantum noises, we show that global error mitigation has no advantage over local error mitigation.

Jiaqing Jiang, Kun Wang, Xin Wang

Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general quantum maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ingredients in quantum information, both in theoretical and practical perspectives. It motivates how well one can approximate a general quantum map by physically implementable operations. In this work, we introduce a systematic framework to resolve this task using the quasiprobability decomposition technique. More specifically, we decompose a target quantum map into a linear combination of physically implementable operations and introduce the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain. We show this measure is efficiently computable by semidefinite programs and prove several properties of this measure, such as faithfulness, additivity, and unitary invariance. We derive lower and upper bounds in terms of the Choi operator's trace norm and obtain analytic expressions for several quantum maps of practical interests. Furthermore, we endow this measure an operational meaning within the quantum error mitigation scenario, quantifying the ultimate sampling cost achievable using the full expressibility of quantum computers. In particular, for parallel quantum noises, we show that global error mitigation has no advantage over local error mitigation.

Mark Kon

Stephen J. Gustafson, Israel Michael Sigal

Tetra Engdahl, Rafael Bachiller Soler, Nuwan J. G. Kankanamge +1 more

Physical layer security (PLS) leverages physical characteristics of wireless channels to allow secure data transfer in wireless communications. While PLS has received considerable research, its practical implementation is still evolving. To address this gap, this work designs and implements a keyless PLS-based communication scheme using three USRP devices in an over-the-air environment in which a multi-antenna transmitter infuses an artificial Gaussian noise source to the nullspace of an intended receiver in order to obscure the received signal of an eavesdropper. The design is applicable to high-order quadrature amplitude modulation (QAM) constellations, which is suitable for high-spectral efficiency wireless communication systems. Our measurement results fully demonstrate the confidentiality achieved by the proposed PLS implementation.