[论文解读] The Quantum Frontier

Joseph F. Fitzsimons, Eleanor Rieffel+1 more|arXiv (Cornell University)|Jun 4, 2012

Quantum Mechanics and Applications参考文献 22被引用 3

一句话总结

本文探討了量子資訊處理的基礎原理，主張量子力學支撐了一種新的運算、通訊與密碼學範式。它表明，即使在沒有完整規模量子硬體的情況下，量子力學的內在隨機性與糾纏態也能帶來超越古典極限的計算優勢，並指出關於量子優勢來源的開放性問題。

ABSTRACT

The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.

研究动机与目标

• 將運算重新定義為量子物理過程，而非古典過程。
• 澄清關於量子現象（如疊加與糾纏）的誤解。
• 研究量子力學如何促成新演算法、密碼學與通訊協定。
• 探討隨機性與非定域性在量子資訊處理中的角色。
• 識別關於量子運算能力根本來源的開放性問題。

提出的方法

• 使用測量的操作性定義來分析量子測量過程。
• 應用貝爾不等式以證明與古典物理不相容的非定域關聯。
• 分析如 Bernstein-Vazirani 演算法，以展示即使無糾纏態也能實現查詢複雜度優勢。
• 回顧量子金鑰分發（BB84）以說明無需糾纏態的實際應用。
• 檢視基於測量的量子計算，以顯示過度糾纏可能妨礙效能。
• 考慮量子力學的假設性修改，以評估其對運算能力的影響。

实验结果

研究问题

• RQ1 內在隨機性在量子力學中扮演何種角色？它與古典不可預測性有何差異？
• RQ2 貝爾不等式的違反如何證明量子關聯的非古典性質？
• RQ3 糾纏態在多大程度上是量子運算加速所必需的？
• RQ4 若量子力學略為非線性或公理被修改，會產生何種運算後果？
• RQ5 哪些基本原理支撐了量子資訊處理的運算能力？

主要发现

• 量子力學展現出無法被拉普拉斯惡魔預測的內在隨機性，顯示絕對不可預測性。
• 貝爾不等式的違反提供了強有力證據，顯示非定域量子關聯與局域隱變量理論不相容。
• 如 Bernstein-Vazirani 的量子演算法可在無糾纏態的情況下實現指數級查詢加速，顯示糾纏態並非總是必需。
• 如 BB84 之類的協定可在無需使用糾纏態的情況下提供資訊理論安全性，展現實際的量子優勢。
• 高度糾纏的量子態在基於測量的量子計算中可能產生負面影響，顯示糾纏態是一種需謹慎管理的資源。
• 假設性修改量子力學（如非線性或公理變更）將導致 #P 與 PP 等困難複雜度類別在多項式時間內解決，暗示量子力學可能受運算限制所約束。