Related papers: One-shot lossy quantum data compression
Lossy data compression lies at the heart of modern communication and storage systems. Shannon's rate-distortion theory provides the fundamental limit on how much a source can be compressed at a given fidelity, but it assumes infinitely long…
In this paper, we consider the one-shot version of the classical Wyner-Ziv problem where a source is compressed in a lossy fashion when only the decoder has access to a correlated side information. Following the entropy-constrained…
Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy…
This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…
This paper introduces the notion of soft bits to address the rate-distortion optimization for learning-based image compression. Recent methods for such compression train an autoencoder end-to-end with an objective to strike a balance…
The source-coding problem with side information at the decoder is studied subject to a constraint that the encoder---to whom the side information is unavailable---be able to compute the decoder's reconstruction sequence to within some…
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of…
We obtain a lower bound on the maximum number of qubits, $Q^{n, \epsilon}(\mathcal{N})$, which can be transmitted over $n$ uses of a quantum channel $\mathcal{N}$, for a given non-zero error threshold $\epsilon$. To obtain our result, we…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
Quantum random variable, distortion operator are introduced based on canonical operators. As the lower bound of rate distortion, the entanglement information rate distortion is achieved by Gaussian map for Gaussian source. General Gaussian…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…
In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…
Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent…
We give an operational meaning to the min-entropy of a quantum state as a resource measure for various interconnected tasks. In particular, we show that the min-entropy without smoothing measures the amount of quantum information that can…
Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the…
Suppose that a quantum source is known to have von Neumann entropy less than or equal to S but is otherwise completely unspecified. We describe a method of universal quantum data compression which will faithfully compress the quantum…
Quantum capacity gives the fundamental limit of information transmission through a channel. However, evaluating the quantum capacities of a continuous-variable bosonic quantum channel, as well as finding an optimal code to achieve the…
In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…
We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an…