The necessary and sufficient condition for perfect teleportation and superdense coding and all the suitable states for teleportation and superdense coding

IF 3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Annals of Physics Pub Date : 2026-05-01 Epub Date: 2026-02-09 DOI:10.1016/j.aop.2026.170377

Dafa Li

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引用次数: 0

Abstract

It is known that two local unitaries (LU) equivalent states possess the same amount of entanglement and can be used to perform the same tasks in quantum information theory (QIT). For a protocol for a task in QIT, we call a protocol LU invariant if two LU-equivalent states are either both suitable for the protocol or neither is. So far, no one has discussed whether a protocol for a task in QIT is LU invariant. In Agrawal and Pati (2006) proposed the perfect teleportation protocol (PTP) and the protocol for superdense coding to transmit 2-bit classical information by sending one qubit (PSDC-2) and 3-bit classical information by sending two qubits (PSDC-3). In this paper, we show that PTP and PSDC-2 are LU invariant. That is, two LU equivalent states are suitable for PTP and PSDC-2 or neither of them is. We show that PSDC-3 is not LU invariant. We also indicate that the teleportation proposed in Nielsen and Chuang (2000) is not LU invariant. We give a necessary and sufficient condition for a state to be suitable for PTP, PSDC-2, and PSDC-3, respectively. Via the LU invariance of PTP and PSDC-2, we prove that a state is suitable for PTP and PSDC-2 if and only if it has 1 ebit of shared entanglement, respectively and find all genuine entangled states and separable states which are suitable for PTP and PSDC-2, respectively. So far, no one has indicated that PTP and PSDC-2 do not require genuine entanglement. Agrawal and Pati suggested to study if there are subclasses of W SLOCC class which are suitable for PSDC-3. So far, it still remains an unsolved question. We show that any state of the SLOCC class W is not suitable for PSDC-3.

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完美的隐形传态和超密编码的充分必要条件和所有适合隐形传态和超密编码的状态

在量子信息理论（QIT）中，已知两个局部酉等效态具有相同的纠缠量，可以用来执行相同的任务。对于QIT中任务的协议，如果两个等效的LU状态都适合该协议，或者都不适合该协议，我们称该协议为LU不变量。到目前为止，还没有人讨论过QIT中任务的协议是否具有LU不变性。Agrawal和Pati（2006）提出了完善的隐形传态协议（PTP）和发送一个量子比特（PSDC-2）传输2位经典信息和发送两个量子比特（PSDC-3）传输3位经典信息的超密集编码协议。本文证明了PTP和PSDC-2是LU不变量。即PTP和PSDC-2有两种LU等效状态，或者两者都不适合。我们证明了PSDC-3不是LU不变的。我们还指出Nielsen和Chuang（2000）提出的隐形传态不是LU不变的。我们分别给出了PTP、PSDC-2和PSDC-3适合状态的充分必要条件。通过PTP和PSDC-2的LU不变性，证明了一个状态分别当且仅当PTP和PSDC-2具有1 ebit的共享纠缠时是适合的，并找到了适合PTP和PSDC-2的所有真实纠缠态和可分离态。到目前为止，还没有人表明PTP和PSDC-2不需要真正的纠缠。Agrawal和Pati建议研究W SLOCC类中是否存在适合PSDC-3的亚类。到目前为止，这仍然是一个未解决的问题。我们证明了SLOCC类W的任何状态都不适合PSDC-3。

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来源期刊

Annals of Physics 物理-物理：综合

CiteScore

5.30

自引率

3.30%

发文量

211

审稿时长

47 days

期刊介绍： Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.