相关论文: No quantum Ramsey theorem for stabilizer codes
We consider a reducible unitary representation of Heisenberg-Weyl group in a tensor product of two Hilbert spaces. A non-commutative operator graph generated by this representation is introduced. It is shown that spectral projections of…
Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer…
Alice and Bob receive a bipartite state (possibly entangled) from some finite collection or from some subspace. Alice sends a message to Bob through a noisy quantum channel such that Bob may determine the initial state, with zero chance of…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. The resulting maps are bistochastic but in general no longer mixed unitary. We analyze their important…
Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a…
Hypergraph states of many quantum bits share the rich interplay between simple combinatorial description and nontrivial entanglement properties enjoyed by the graph states that they generalize. In this paper, we consider hypergraph states…
The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code…
We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in…
The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for…
The Gottesman-Knill theorem allows for the efficient simulation of stabilizer-based quantum error-correction circuits. Errors in these circuits are commonly modeled as depolarizing channels by using Monte Carlo methods to insert Pauli gates…
It is known that nonadditive quantum codes are more optimal for error correction when compared to stabilizer codes. The class of codeword stabilized codes (CWS) provides tools to obtain new nonadditive quantum codes by reducing the problem…
Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a…
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…
We solve one of the oldest problems in the theory of quantum stabilizer codes by proving the non-existence of quantum [[13,5,4]]-codes.
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…