SEPARABILITY OF VERY NOISY MIXED STATES AND IMPLICATIONS FOR NMR QUANTUM COMPUTING

@article{Braunstein1999SEPARABILITYOV,
  title={SEPARABILITY OF VERY NOISY MIXED STATES AND IMPLICATIONS FOR NMR QUANTUM COMPUTING},
  author={Samuel L. Braunstein and Carlton M. Caves and Richard Jozsa and Noah Linden and Sandu Popescu and R{\"u}diger Schack},
  journal={Physical Review Letters},
  year={1999},
  volume={83},
  pages={1054-1057}
}
We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable (unentangled). The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. The bounds show that no entanglement appears in the physical states at any stage of present NMR… 
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References

SHOWING 1-10 OF 53 REFERENCES
Volume of the set of separable states
The question of how many entangled or, respectively, separable states there are in the set of all quantum states is considered. We propose a natural measure in the space of density matrices %
Robustness of entanglement
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is
Power of One Bit of Quantum Information
In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial
Ensemble quantum computing by NMR spectroscopy
TLDR
A new computational model is presented, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof, which can solve nondeterministic polynomial-time complete problems inPolynomial time.
Bulk quantum computation with nuclear magnetic resonance: theory and experiment
We show that quantum computation is possible with mixed states instead of pure states as inputs. This is performed by embedding within the mixed state a subspace that transforms like a pure state and
Experimental realization of a quantum algorithm
Quantum computers can in principle exploit quantum-mechanical effects to perform computations (such as factoring large numbers or searching an unsorted database) more rapidly than classical
Purification of noisy entanglement and faithful teleportation via noisy channels.
TLDR
Upper and lower bounds on the yield of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$ are given, showing $D(M)>0$ if $\bra{Psi-}M\ket-}>\half$.
Bulk Spin-Resonance Quantum Computation
TLDR
A new approach to quantum computing is introduced based on the use of multiple-pulse resonance techniques to manipulate the small deviation from equilibrium of the density matrix of a macroscopic ensemble so that it appears to be the density Matrix of a much lower dimensional pure state.
Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer
TLDR
This work demonstrates the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions).
Bell’s theorem without inequalities
It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the
...
...