Noise effects on purity and quantum entanglement in terms of physical implementability

Abstract

Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels. However, there is no explicit relation between the decoherence effect induced by a noise channel and its error rate. In this work, we propose to characterize the decoherence effect of a noise channel by the physical implementability of its inverse, which is a universal parameter quantifying the difficulty to simulate the noise inverse with accessible quantum channels. We establish two concise inequalities connecting the decrease of the state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse, which is required to be decomposed as mutually orthogonal unitaries or product channels respectively. Our results are numerically demonstrated on several commonly adopted two-qubit noise models. We believe that these relations contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.

19 pages, 3 figure

References in corpus (13)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Entanglement detection
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement versus Correlations in Spin Systems
• Localizable Entanglement
• Cost of quantum entanglement simplified
• Quantum error mitigation via matrix product operators
• Entanglement entropy production in Quantum Neural Networks
• Fundamental Limitation on the Detectability of Entanglement
• Qubit noise deconvolution
• NISQ: Error Correction, Mitigation, and Noise Simulation
• Skew information-based coherence generating power of quantum channels
• Noisy induced entanglement transition in one-dimensional random quantum circuits

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• Compressed quantum error mitigation
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• Feed-Forward Probabilistic Error Cancellation with Noisy Recovery Gates