Guesswork with Quantum Side Information

State transfer with quantum side information

We first consider quantum communication protocols between a sender Alice and a receiver Bob, which transfer Alice's quantum information to Bob by means of non-local resources, such as classical communication, quantum communication, and entanglement. In these protocols, we assume that Alice and Bob may have quantum side information, not transferred. In this work, these protocols are called the state transfer with quantum side information. We determine the optimal costs for non-local resources in the protocols, and study what the effects of the use of quantum side information are. Our results ca…

Side information -driven quantum composite control for protecting a qubit

We study protection of a qubit that transfer through a decoherence noise by quantum control technique. In this work, we assume that the communication participants have some side information about the qubit. Our aim is to take fully advantage of given side information to design a quantum control scheme that makes the output state close to the input state as better as possible. Especially, in this paper, we consider the quantum composite control (QCC) structure, which has shown to capture a better balance between fidelity and success probability, i.e., two essential measures for protection. Comp…

Channel simulation with quantum side information

We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classical-quantum Slepian-Wolf problem. The optimal noiseless communication rate is found to be reduced from the mutual information between the channel input and output by the Holevo information between the channel output and the quantum side information. Our main theorem has two important corollaries. The first is a quantum generalization of the Wyner-Ziv problem: rate-distortion theory with quantum side i…

Leftover Hashing Against Quantum Side Information

The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is (usually implicitly) defined with respect to classical side information. Here, we prove a (strictly) more general version of the Leftover Hash Lemma that is valid even if side information is represented by the state of a quantum system. Furthermore, our result applies to arbitrary delta-almost two-universal families of hash functions. The generalized Leftover…

利用经典侧信息的电路切割

Circuit cutting with classical side information

本研究通过量子仪器形式化了利用经典侧信息的通用电路切割技术，分析了其在减少采样开销上的优势，并提出了可通过半定规划高效评估的最优采样开销下界。

Coding for quantum channels with side information at the transmitter

We consider the problem of coding for quantum channels with side information that is available ahead of time at the transmitter but not at the receiver. We find a single-letter expression for the entanglement-assisted quantum capacity of such channels which closely parallels Gel'fand and Pinsker's solution to the classical version of the same problem. This theorem can also be used to find a lower bound on the unassisted quantum capacity of these channels.

One-Shot Classical Data Compression with Quantum Side Information and the Distillation of Common Randomness or Secret Keys

The task of compressing classical information in the one-shot scenario is studied in the setting where the decompressor additionally has access to some given quantum side information. In this hybrid classical-quantum version of the famous Slepian-Wolf problem, the smooth max-entropy is found to govern the number of bits into which classical information can be compressed so that it can be reliably recovered from the compressed version and quantum side information. Combining this result with known results on privacy amplification then yields bounds on the amount of common randomness and secret k…

针对量子边信息的改进双源提取器

Improved Two-source Extractors against Quantum Side Information

本文证明了 Dodis 等人的双源提取器在面对量子边信息时性能与经典领域同样出色，并推导出新量子 XOR 引理以重新推导通用归约并改进一大类提取器。

Quantum from principles

Quantum theory was discovered in an adventurous way, under the urge to solve puzzles-like the spectrum of the blackbody radiation-that haunted the physics community at the beginning of the 20th century. It soon became clear, though, that quantum theory was not just a theory of specific physical systems, but rather a new language of universal applicability. Can this language be reconstructed from first principles? Can we arrive at it from logical reasoning, instead of ad hoc guesswork? A positive answer was provided in Refs. [1, 2], where we put forward six principles that identify quantum theo…

带边信息的多链路集中式测量压缩

Centralised multi link measurement compression with side information

本文提出带量子边信息的集中式多链路测量压缩问题，给出无需催化随机性的近最优一次性可达性界，并推广至渐近iid情形，核心工具是新颖的序贯经典量子多部分覆盖引理。

Entanglement-Assisted Capacity of Quantum Channels with Side Information

Entanglement-assisted communication over a random-parameter quantum channel with either causal or non-causal channel side information (CSI) at the encoder is considered. This describes a scenario where the quantum channel depends on the quantum state of the input environment. While Bob, the decoder, has no access to this state, Alice, the transmitter, performs a sequence of projective measurements on her environment and encodes her message accordingly. Dupuis established the entanglement-assisted capacity with non-causal CSI. Here, we establish characterization in the causal setting, and also …

Side-Information Coding with Turbo Codes and its Application to Quantum Key Distribution

Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its application to the reconciliation problem occurring in a continuous-variable quantum key distribution protocol.