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Correcting Quantum Errors with Entanglement
TLDR
The entanglement-assisted quantum codes described do not require the dual-containing constraint necessary for standard quantum error–correcting codes, thus allowing us to “quantize” all of classical linear coding theory.
Quantum Computing
  • T. Brun
  • Computer Science
    Computer Science, The Hardware, Software and…
  • 2011
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 to
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 time
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. I
Entanglement increases the error-correcting ability of quantum error-correcting codes
TLDR
This work shows how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a regular quantum stabilizer code, over different encoding operators.
Quantum to classical transition for random walks.
TLDR
The position variance is used as an indicator of classical behavior and it is seen that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth ofThe variance even for weakDecoherence.
Quantum walks with infinite hitting times
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite.
Quantum Error Correction
  • T. Brun
  • Computer Science, Physics
    Oxford Research Encyclopedia of Physics
  • 8 October 2019
TLDR
In quantum computation, error correction is just one component of fault-tolerant design; other approaches to error mitigation in quantum systems include decoherence-free subspaces, noiseless subsystems, and dynamical decoupling.
Weak measurements are universal.
TLDR
It is shown that any measurement can be generated by weak measurements, and hence that weak measurements are universal, and may have important applications to the theory of entanglement.
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