Related papers: The Spectrum of Quantum Caps in PG(4,4)
Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing…
Subsystem codes are a generalization of noiseless subsystems, decoherence free subspaces, and quantum error-correcting codes. We prove a Singleton bound for GF(q)-linear subsystem codes. It follows that no subsystem code over a prime field…
The main result in this paper is the proof of the recently conjectured non-existence of cubic Legendre multiplier sequences. We also give an alternative proof of the non-existence of linear Legendre multiplier sequences, using a method that…
The unitarity problem in curved spacetime is solved for the string described by the SL(2,R) WZW model. The spectrum is computed exactly and demonstratedto be ghost-free. The new features include (i) SL(2,R) left/right symmetrycurrents that…
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…
The existence is proved of a class of open quantum systems that admits a linear subspace ${\cal C}$ of the space of states such that the restriction of the dynamical semigroup to the states built over $\cal C$ is unitary. Such subspace…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
The signless Laplacian spectral radius has emerged as a crucial spectral parameter in network science. This paper establishes new extremal results in spectral graph theory by investigating the signless Laplacian spectral radius ($Q$-index)…
We establish some properties of quantum limits on a product manifold, proving for instance that, under appropriate assumptions, the quantum limits on the product of manifolds are absolutely continuous if the quantum limits on each manifolds…
For every $n = 2^k > 8$ there exist exactly $[(k+1)/2]$ mutually nonequivalent $Z_4$-linear extended perfect codes with distance 4. All these codes have different ranks.
We prove that a certain binary linear code associated with the incidence matrix of a quasi-symmetric 2-(37,9,8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even self-dual code of length 40. Using the…
We consider a pair of linear operators corresponding to the linearization around the ground state soliton of the cubic nonlinear Schr\"odinger equation in dimension three. We introduce a new comparison-based approach and rigorously prove…
We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge…
We study perfect codes in the sum-rank metric, a generalization of both the Hamming and rank metrics relevant in multishot network coding and space-time coding. A perfect code attains equality in the sphere-packing bound, corresponding to a…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasi-symmetric 2-$(56,12,9)$ and 2-$(57,12,11)$ designs with intersection numbers 0 and 3, and the…
Finite-size criteria have emerged as an effective tool for deriving spectral gaps in higher-dimensional frustration-free quantum spin systems. We quantitatively improve the existing finite-size criteria by introducing a novel subsystem…
The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. However, standard error correction refers to abstract quantum…
The paper introduces new bounds on the asymptotic density of parity-check matrices and the achievable rates under ML decoding of binary linear block codes transmitted over memoryless binary-input output-symmetric channels. The lower bounds…