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arXiv:2307.07952 · Quantum Information Processing

Theoretical proposal for the experimental realization of realignment operation

Shruti Aggarwal, Satyabrata Adhikari

Published Jun 1, 2024• 4 citations
arXivHTMLPDF
DOI
10.1007/s11128-024-04422-w

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Physical experiments and computation

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We experimentally investigate the one-shot distillation of quantum coherence, which focuses on the transformations from a single copy of a given state into maximally coherent states under various incoherent operations. We present a general proposal to realize a type of strictly incoherent operations (SIOs) that can act on N -dimensional ( N ≥ 2 ) states. This proposal is suitable for a variety of quantum devices. Based on a linear optical setup, we experimentally demonstrate that the proposed SIO successfully implements pure-to-pure state transformations, and thus the one-shot coherence distillation process is accomplished. The experimental data agree well with the theoretical results and clearly indicate the distillation fidelities, which bound the regions of different coherence distillation rates versus different superposition parameters of input states and different distillation errors.
The efficient detection of quantum entanglement is a central problem in quantum information processing. This paper systematically proposes a quantum circuit implementation scheme based on the Positive Partial Transpose (PPT) and the Computable Cross-Norm Realignment (CCNR) criteria, providing a complete quantum algorithmic pathway for efficient and computable entanglement detection. By encoding quantum states into specific forms and utilizing SWAP operations, complex matrix operations such as partial transpose and realignment are transformed into executable quantum circuits. Furthermore, by integrating an improved variational quantum singular value decomposition subroutine, the scheme enables the efficient estimation of the trace norm, thereby determining the existence of entanglement. Designed to operate within a hybrid quantum-classical framework, this scheme exhibits excellent scalability and practicality, offering a theoretical tool and methodological support for analyzing the entanglement structure of complex quantum systems on future intermediate-scale quantum devices.
Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing. However, detecting it in mixed quantum states remains a challenging task. While the positive partial transposition (PPT) and computable cross-norm and realignment criteria are well-established tools for entanglement detection in general, and are especially effective in Bell-diagonal states, their connection to the underlying group structure of this state family has not been fully explored. In this work, we analyze the PPT and realignment criteria for Bell-diagonal states from a group-theoretic point of view. Our results demonstrate that the group structure of Bell-diagonal states provides a clear framework for analyzing and computing these two entanglement-detection criteria, thereby highlighting the connection between entanglement and group structure. This unified perspective offers insights into the mathematical and physical properties of entanglement in structured quantum systems and ties the PPT and realignment criteria for Bell-diagonal states to experimental procedures.