測試訊息因果論在量子通訊中的正確性

Abstract

在基於物理理論的通訊協定中, 例如:量子力學, 訊息因果論限制傳送者與 接受者之間的最大共有訊息量. 我們通過更廣泛的框架, 即使用討論訊號傳送及錯誤計算的結果, 來重新 了解訊息因果論與量子力學的關係. 在我們的框架中, 訊息因果論將導致一組 在二態量子系統下的Tsirelson 不等式 (量子系統的極限值). 基於這樣的結 果, 訊息因果論對使用物理系統的實驗產生限制. 此外, 在我們的框架中, 可 信賴的非定域性的計算是不可行的. 訊息因果論的限制將使得物理系統的計算 線路無法進行可信賴的計算. 另外, 我們直接計算共有訊息量, 藉以測試訊息因果論在更普遍的通訊協 定中的正確性, 這些普遍的通訊協定包含多態的系統及非對稱的通訊管道. 我 們的結果支持訊息因果論, 意思是在這些普遍的通訊協定中, 共有訊息量不會 超過訊息因果論給的限制. 此外, 如果通訊管道包含兩個輸出及兩個輸入, 我 們發現共有的量子系統擁有最大非定域性時 (滿足Tsirelson 不等式的限制), 共有訊息量的值不是最大的. 最大的共有訊息量出現在共有的系統恰好滿足定 域性理論給出的極大值時 (Bell 不等式給的限制), 且此時共有的訊息量和訊 息因果論給的限制相同. 這個結果指出共享一個量子非定域系統, 並不一定產 生較多的共有訊息量.Information causality has been proposed to constrain the maximal mutual information shared between sender and receiver in a communication protocol based on physical theories such as quantum mechanics.

We reformulate the information causality in a more general framework by adopting the results of signal propagation and computation in a noisy circuit. In our framework, the information causality leads to a broad class of Tsirelson inequalities for the two-level quantum systems. This fact allows us to subject the information causality to the experimental scrutiny. A no-go theorem for reliable nonlocal computation is also derived. Information causality prevents any physical circuit from performing reliable computations.

Moreover, we test the information causality for the more general quantum communication protocols with multi-level and (non-)symmetric channels by directly evaluating the mutual information. Our results support the information causality which is never violated for the more general settings discussed in this work. For the two-inputs/two-outputs cases, we also find that the information causality is saturated not for the channels with the maximal quantum non-locality associated with the Tsirelson inequality but for the marginal cases saturating the Bell's inequality. This indicates that the more quantum non-locality may not always yield the more mutual information.