--- title: "密集编码：三种消息与一份资源账本" description: "1996 年三消息实验与理想四态协议，各自展示了什么？" canonical_url: "https://sandboxphysics.com/zh/stories/quantum-evidence/dense-coding-three-messages-resources/" language: "zh-CN" page_type: "story" alternate_languages: en: "https://sandboxphysics.com/stories/quantum-evidence/dense-coding-three-messages-resources/" last_modified: "2026-10-18" --- [量子物理：读懂证据](https://sandboxphysics.com/zh/stories/quantum-evidence/) 诺奖 A · 证据与操控 # 密集编码：三种消息与一份资源账本 Sandbox Physics · 2026-10-18 1996 年三消息实验与理想四态协议，各自展示了什么？ ## 先数实际分开的消息 Mattle 等人在 1996 年使用偏振纠缠光子，对其中一个作局域编码，再用联合光学分析器读出，演示三符号字母表。所选字符演示每个字符用五个三进制位，并非可靠分辨四种 Bell 消息。五个三进制位只能表示 243 种码字，少于八比特的 256 种模式；展示的字符可以容纳，却不是全部八比特值的通用定长转换。 理论编码空间可能大于分析器可分辨的结果数，这一区别很关键。原探测安排单独区分两种 Bell 态，却把另外两种合成一类；附加分束安排使第三类可被登记，但探测率更低。 证据阅读：K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy ## 四种编码先要共享一对 理想教学协议先取双水平与双竖直的正号 Bell 叠加。在其中一个成员上施加恒等、比特翻转、相位翻转或两者组合，可得四个相互正交的 Bell 态，允许无关的整体相位。 发送方随后必须把该成员实际送给接收方，后者已持有另一个成员，并进行联合测量。无论怎样编码，接收方原有单光子局部态都为最大混合态。预先共享纠缠与所传量子比特都是资源，核算通信优势时不能省掉任一项。 证据阅读：C. H. Bennett and S. J. Wiesner (1992), Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states — IBM author record and abstract K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy ## 字母表大小不等于送达信息 理想无误接收器中，三种等概率消息的每个接受符号携带以二为底的三的对数，约 1.585 比特。四种完全可分、等概率消息则为两比特。字母使用不均会降低输入熵。 更一般的量是下式所示的消息与探测输出之间的互信息，并要给出概率分布。对数以二为底，零概率项省略。字母表非空，并不保证探测结果能辨认消息。 $$ I(M;D)=\sum_{m,d}p(m,d)\log_2\!\frac{p(m,d)}{p(m)p(d)} $$ 证据阅读：C. H. Bennett and S. J. Wiesner (1992), Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states — IBM author record and abstract K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy ## 试算两种不同的信道账本 自己构造一个三字母对称信道：正确输出概率为 0.90，两种错误字母各为 0.05。均匀输入时输出仍均匀，但每试次互信息只有约 1.016 比特。只数标签会高估送达信息。 另一个虚拟信道在成功时完全正确，却有与消息无关的二分之一擦除概率。把擦除保留为输出，每次尝试约传 0.792 比特，而接受子集仍为每个接受符号 1.585 比特。两者分母不同，这些算例没有重建 1996 年装置。 证据阅读：K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy ## 归一化曲线可能藏起接收差异 历史字符图把每种登记类别分别除以自身最大值，使消息顺序容易辨认，却不是等效率计数账本。论文还说明了附加第三类探测配置较低的登记概率。 评价实际信道时，要保留编码尝试、全部登记输出、擦除与采集时间。若接收概率依赖消息，连接受子集的输入分布也会改变。混淆矩阵和资源预算能回答三条干净归一化峰无法解决的问题。 证据阅读：K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy ## 使用要素时保留各自结论 密集编码不能只靠纠缠发送指定消息；传送成员与联合读出才使消息可得。优势比较针对明确通信资源，若再计入制对、分发、稳定与探测所用的全部光子，则是更广的工程预算。 单比特和 Hong–Ou–Mandel Lab 可分别检查局域操作与双光子干涉，并未实现这套密集编码信道或复现其效率。应先把三消息结果读成具有明确分析器的光学演示，再与理想四态资源约定比较。 证据阅读：C. H. Bennett and S. J. Wiesner (1992), Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states — IBM author record and abstract K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy ## 接着操作模型 以下为已有教学 Lab；其模拟记录与上文历史观测分别对待。 - [检查单比特旋转](https://sandboxphysics.com/zh/labs/qubit-state/) - [比较分析器所用的双光子干涉](https://sandboxphysics.com/zh/labs/hong-ou-mandel/) ## 来源与阅读说明 本文从 Illinois 镜像核读 Mattle 等人 1996 年四页 PRL，重点为表一和图四至五。Bennett 与 Wiesner 的 1992 年提案通过 IBM 作者记录及摘要引用，本轮未取得可读全文。正交性、熵和擦除算例均为独立教学计算。 1. [K. Mattle, H. Weinfurter, P. G. Kwiat and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, PRL 76, 4656–4659 — Illinois copy](https://courses.grainger.illinois.edu/phys513/sp2019/reading/week9/Dense_coding_Zeilinger1996.pdf) 2. [C. H. Bennett and S. J. Wiesner (1992), Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states — IBM author record and abstract](https://research.ibm.com/publications/communication-via-one-and-two-particle-operators-on-einstein-podolsky-rosen-states) [黑体辐射：证据是一整条曲线](https://sandboxphysics.com/zh/stories/quantum-evidence/blackbody-spectrum-planck-wien/) [光电效应：电压还不是电子的能量](https://sandboxphysics.com/zh/stories/quantum-evidence/photoelectric-stopping-potential-contact/) [油滴实验：从下落时间里找出电荷单位](https://sandboxphysics.com/zh/stories/quantum-evidence/millikan-oil-drop-charge-inference/) [原子谱：定态的证据，不是轨道的照片](https://sandboxphysics.com/zh/stories/quantum-evidence/atomic-spectra-stationary-states/) [Franck–Hertz：下降的电流能证明什么](https://sandboxphysics.com/zh/stories/quantum-evidence/franck-hertz-discrete-excitation/) [Compton 散射：光还要平衡动量](https://sandboxphysics.com/zh/stories/quantum-evidence/compton-scattering-energy-momentum/) [de 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