Các biện pháp phân biệt hình học giới hạn ước lượng và phân biệt kênh lượng tử

Quantum Information Processing - Tập 20 - Trang 1-170 - 2021
Vishal Katariya1, Mark M. Wilde1,2
1Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, USA
2Stanford Institute for Theoretical Physics, Stanford University, Stanford, USA

Tóm tắt

Ước lượng và phân biệt kênh lượng tử là các nhiệm vụ xử lý thông tin có liên quan cơ bản mà được quan tâm trong khoa học thông tin lượng tử. Trong bài báo này, chúng tôi phân tích các nhiệm vụ này bằng cách sử dụng thông tin Fisher đạo hàm logarit phải đúng và entropy tương đối Rényi hình học, đồng thời chúng tôi cũng xác định mối liên hệ giữa các biện pháp phân biệt này. Một kết quả chính trong bài báo của chúng tôi là tính chất chuỗi giữ nguyên đối với thông tin Fisher đạo hàm logarit phải đúng và entropy tương đối Rényi hình học cho khoảng $$\alpha \in (0,1)$$ của tham số Rényi $$\alpha$$. Trong ước lượng kênh, những kết quả này gợi ý một điều kiện cho việc không đạt được sự mở rộng Heisenberg, trong khi trong phân biệt kênh, chúng dẫn đến các ràng buộc cải thiện về tỷ lệ lỗi trong các cài đặt exponent lỗi Chernoff và Hoeffding. Nói chung hơn, chúng tôi giới thiệu thông tin Fisher lượng tử tính toán được như một khung ý tưởng để phân tích các giao thức tuần tự tổng quát ước lượng một tham số được mã hóa trong một kênh lượng tử. Chúng tôi sau đó sử dụng khung này, ngoài ứng dụng đã đề cập, để chỉ ra rằng sự mở rộng Heisenberg là không thể khi một tham số được mã hóa trong một kênh cổ điển – lượng tử. Chúng tôi cũng xác định một số mối liên hệ khác về khái niệm và kỹ thuật giữa các nhiệm vụ ước lượng và phân biệt và các biện pháp phân biệt liên quan trong phân tích mỗi nhiệm vụ. Là một phần của công việc này, chúng tôi trình bày một cái nhìn tổng quan chi tiết về entropy tương đối Rényi hình học của các trạng thái và kênh lượng tử, cũng như các thuộc tính của nó, có thể gây được sự quan tâm độc lập.

Từ khóa

#kênh lượng tử #ước lượng kênh #phân biệt kênh #thông tin Fisher #entropy tương đối Rényi hình học

Tài liệu tham khảo

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