Related papers: Generalized Perfect Codes for Symmetric Classical-…
The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present…
Quantum cloning is a fundamental protocol of quantum information theory. Perfect universal quantum cloning is prohibited by the laws of quantum mechanics, only imperfect copies being reachable. Symmetric quantum cloning is concerned with…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
We derive universal codes for transmission of broadcast and confidential messages over classical-quantum-quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
We show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion of success in transmission, and that which uses the minimum fidelity of pure states in a subspace of…
For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify in…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for…
Quantum key distribution (QKD) systems require optimal performance of both quantum and classical channels - utilizing as few as possible qubits and bits for establishing as many as possible key bits. Here we report a way to determine if a…
Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines…
Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…
We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for…