Related papers: Lossless quantum data compression with exponential…
Analytically continuing the von Neumann entropy from R\'enyi entropies is a challenging task in quantum field theory. While the $n$-th R\'enyi entropy can be computed using the replica method in the path integral representation of quantum…
The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
In this article we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared…
We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this…
Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Finite-size general security proofs for quantum key distribution based on R\'enyi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
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…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size…
We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in…
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect,…
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…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…