Related papers: Entanglement-assisted codeword stabilized quantum …
Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…
Though the no-cloning theorem [1] prohibits exact replication of arbitrary quantum states, there are many instances in quantum information processing and entanglement measurement in which a weaker form of cloning may be useful. Here, I…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
Quantum entanglement plays a crucial role in quantum computing. Entangling information has important implications for understanding the behavior of quantum programs and avoiding entanglement-induced errors. Entanglement analysis is a static…
Entanglement distillation, the process of converting weakly entangled states into maximally entangled ones using Local Operations and Classical Communication (LOCC), is pivotal for robust entanglement-assisted quantum information processing…
We discuss quantum key distribution protocols using quantum continuous variables. We show that such protocols can be made secure against individual gaussian attacks regardless the transmission of the optical line between Alice and Bob. This…
A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
Solid state qubits realized in superconducting circuits are potentially extremely scalable. However, strong decoherence may be transferred to the qubits by various elements of the circuits that couple individual qubits, particularly when…
In this paper we fill the gap in previous works by proving the formula for entanglement-assisted capacity of quantum channel with additive constraint (such as bosonic Gaussian channel). The main tools are the coding theorem for…
We report the first nonadditive quantum error-correcting code, namely, a $((9,12,3))$ code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
In this paper I explore the entanglement evolution of qubits that are part of a five qubit quantum error correction code subject to various decohering environments. Specifically, I look for possible parallels between the entanglement…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the…
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We show that if no entanglement is envolved then…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…