相关论文: Classical Coding and the Cauchy-Schwarz Inequality

The problem of computing distances of error-correcting codes is fundamental in both the classical and quantum settings. While hardness for the classical version of these problems has been known for some time (in both the exact and…

This thesis investigates quantum cloning and related quantum entanglement problems using core concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its…

Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…

We construct new polar coding schemes for the transmission of quantum or private classical information over arbitrary quantum channels. In the former case, our coding scheme achieves the symmetric coherent information and in the latter the…

The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…

The quantum analogues of classical variable-length codes are indeterminate-length quantum codes, in which codewords may exist in superpositions of different lengths. This paper explores some of their properties. The length observable for…

We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…

One of the primary goals of information theory is to provide limits on the amount of information it is possible to send through various types of communication channels, and to understand the encoding methods that will allow one to achieve…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…

We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…

The no-cloning theorem leads to information-theoretic security in various quantum cryptographic protocols. However, this security typically derives from a possibly weaker property that classical information encoded in certain quantum states…

A family of quantum cloning machines is introduced that produce two approximate copies from a single quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, describing…

We propose a quantum copy-protection system which protects classical information in the form of non-orthogonal quantum states. The decryption of the stored information is not possible in the classical representation and the decryption…

In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in Quantum Field Theory.…

We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…

We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is…

Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical"…

In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum…