Related papers: Lower Bounds on the Quantum Capacity and Highest E…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
In digital systems such as fiber optical communications, the ratio between probability of errors of type $1\to 0$ and $0 \to 1$ can be large. Practically, one can assume that only one type of error can occur. These errors arecalled…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
In this paper, we bound the rate of linear codes in $\mathbb{F}_q^n$ with the property that any $k\leq q$ codewords are all simultaneously distinct in at least $d_k$ coordinates. For the case of particular interest $q=k=3$ we recover, with…
We consider a molecular channel, in which messages are encoded to the frequency of objects in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling with replacement from the pool.…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite…
We define here a new kind of quantum channel capacity by extending the concept of zero-error capacity for a noisy quantum channel. The necessary requirement for which a quantum channel has zero-error capacity greater than zero is given.…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that…
The exponential server timing channel is known to be the simplest, and in some sense canonical, queuing timing channel. The capacity of this infinite-memory channel is known. Here, we discuss practical finite-length restrictions on the…
We study the robustness of quantum computers under the influence of errors modelled by strictly contractive channels. A channel $T$ is defined to be strictly contractive if, for any pair of density operators $\rho,\sigma$ in its domain, $\|…
It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed that only one…