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arXiv:quant-ph/0509093

Conditional quantum distinguishability and pure quantum communication

Tian-Hai Zeng

Published Sep 14, 2005• 0 citations
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Abstract

I design a simple way of distinguishing non-orthogonal quantum states with perfect reliability using only quantum control-not gates in one condition. In this way, we can implement pure quantum communication in directly sending classical information, Ekert quantum cryptography and quantum teleportation without the help of classical communications channel.

DOI
10.48550/arxiv.quant-ph/0509093

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I design a simple way of distinguishing non-orthogonal quantum states with perfect reliability using only quantum control-not gates in one condition. In this way, we can implement pure quantum communication in directly sending classical information, Ekert quantum cryptography and quantum teleportation without the help of classical communications channel.
This thesis is focused on the design and analysis of quantum communication protocols. Several schemes for quantum communication have been introduced in the recent past. For example, quantum teleportation, dense coding, quantum key distribution, quantum secure direct communication, etc., have been rigorously studied in the last 2-3 decades. Specifically, a specific attention of the present thesis is to study the quantum teleportation schemes with entangled orthogonal and nonorthogonal states and their experimental realization, but not limited to it. We have also studied some aspects of quantum cryptography.
This thesis is focused on the design and analysis of quantum communication protocols. Several schemes for quantum communication have been introduced in the recent past. For example, quantum teleportation, dense coding, quantum key distribution, quantum secure direct communication, etc., have been rigorously studied in the last 2-3 decades. Specifically, a specific attention of the present thesis is to study the quantum teleportation schemes with entangled orthogonal and nonorthogonal states and their experimental realization, but not limited to it. We have also studied some aspects of quantum cryptography.
In a seminal work [PRL85.4972], Walgate, Short, Hardy, and Vedral prove in finite dimensions that for every pair of pure multipartite orthogonal quantum states, there exists a one-way local operations and classical communication (LOCC) protocol that perfectly distinguishes the pair. We extend this result to infinite dimensions with a simpler proof. For states on CdA×dA⊗CdB×dB\mathbb{C}^{d_A \times d_A} \otimes \mathbb{C}^{d_B \times d_B}CdA​×dA​⊗CdB​×dB​, we strengthen this existence result by constructing an O(dA2dB2)O(d_A^2 d_B^2)O(dA2​dB2​)-time algorithm that specifies such a perfect one-way LOCC protocol. Finally, we establish the equivalence between Walgate et al.'s result and the fact that the one-shot environment-assisted classical capacity of every quantum channel is at least 1 bit per channel use, thereby clarifying the literature on these notions. At the core of all of these results is the fact that every operator with vanishing trace admits a basis where its diagonal entries are all zero.
Quantum state that carries classical information, 0 or 1, can be safely and reliably transmitted using quantum secure direct communication. How to transmit an arbitrary quantum state is a wider issue and has important applications. One way is to use quantum teleportation, namely, first distribute a large number of Einstein-Podolsky-Rosen pairs, and then perform entanglement purification to obtain a near-perfect pair, and make quantum teleportation using the pair. In this article, we propose a method that directly port the quantum state with security and reliability using quantum secure direct communication. After sufficient number of copies of the same state have been directly ported, single-particle purification is performed to obtain a near perfect single particle state. This is important because it offers a new method for sending an arbitrary single particle state securely and reliably without using quantum teleportation. It is also an important extension of quantum secure direct communication to send an arbitrary quantum state. Quantum direct portation will have great potential in quantum internet.