• Publications
  • Influence
Correcting Quantum Errors with Entanglement
TLDR
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction, allowing us to “quantize” all of classical linear coding theory. Expand
  • 217
  • 30
  • PDF
Quantum Computing
  • T. Brun
  • Computer Science
  • Computer Science, The Hardware, Software and…
  • 2011
  • 1,641
  • 12
Optimal entanglement formulas for entanglement-assisted quantum coding
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies toExpand
  • 99
  • 9
  • PDF
Quantum Error Correction
  • T. Brun
  • Mathematics, Physics
  • 8 October 2019
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The informationExpand
  • 71
  • 8
  • PDF
Hitting time for quantum walks on the hypercube (8 pages)
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting timeExpand
  • 95
  • 7
  • PDF
A simple model of quantum trajectories
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. IExpand
  • 177
  • 6
  • PDF
Quantum to classical transition for random walks.
We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensionalExpand
  • 124
  • 6
  • PDF
Catalytic Quantum Error Correction
TLDR
We develop the theory of entanglement-assisted quantum error-correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to preshared entanglements. Expand
  • 55
  • 5
  • PDF
Quantum walks driven by many coins
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantumExpand
  • 119
  • 5
  • PDF
Entanglement-assisted quantum error-correcting codes with imperfect ebits
versions of this problem. We rst show that any (nondegenerate) standard stabilizer code can be transformed into an EAQEC code that can correct errors on the qubits of both sender and receiver. TheseExpand
  • 26
  • 5
  • PDF