Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations

@article{Saberi2013GenuineFG,
  title={Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations},
  author={Hamed Saberi},
  journal={Physical Review A},
  year={2013},
  volume={88},
  pages={062315}
}
  • H. Saberi
  • Published 3 June 2013
  • Mathematics
  • Physical Review A
We draw attention to the existence of “genuine” fidelity gaps in an ancilla-assisted sequential decomposition of genuinely entangling isometry and unitary operations of quantum computing. The gaps arise upon a bipartite decomposition of a multiqubit operation in a one-way sequential recipe in which an ancillary system interacts locally and only once with each qubit in a row. Given the known “no-go” associated with such a theoretically and experimentally desirable decomposition, various figures… 

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References

SHOWING 1-10 OF 69 REFERENCES
Ancilla-assisted sequential approximation of nonlocal unitary operations
We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of
Unitary quantum gates, perfect entanglers, and unistochastic maps
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon
Sequential implementation of global quantum operations.
TLDR
It is proved that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example.
Sequential quantum cloning under real-life conditions
We consider a sequential implementation of the optimal quantum cloning machine of Gisin and Massar and propose optimization protocols for experimental realization of such a quantum cloner subject to
Constrained optimization of sequentially generated entangled multiqubit states
We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit
Sequential generation of entangled multiqubit states.
TLDR
This work considers the deterministic generation of entangled multiqubit states by the sequential coupling of an ancillary system to initially uncorrelated qubits and shows, in particular, how to generate familiar quantum information states such as W, Greenberger-Horne-Zeilinger, and cluster states within such a framework.
Entangling and disentangling power of unitary transformations are not equal.
TLDR
It is proved that in large dimensions, almost all bipartite unitaries have entangling and disentangling capacities close to maximal, and that there can be no unique ordering for unitary gates in terms of their ability to perform nonlocal tasks.
Entangling power and operator entanglement in qudit systems
We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on
Two-bit gates are universal for quantum computation.
  • DiVincenzo
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1995
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The
...
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