96 research outputs found
Bounds on relative entropy of entanglement for multi-party systems
We present upper and lower bounds to the relative entropy of entanglement of
multi-party systems in terms of the bi-partite entanglements of formation and
distillation and entropies of various subsystems. We point out implications of
our results to the local reversible convertibility of multi-party pure states
and discuss their physical basis in terms of deleting of information.Comment: 4 pages, no figure
A new class of entanglement measures
We introduce new entanglement measures on the set of density operators on
tensor product Hilbert spaces. These measures are based on the greatest cross
norm on the tensor product of the sets of trace class operators on Hilbert
space. We show that they satisfy the basic requirements on entanglement
measures discussed in the literature, including convexity, invariance under
local unitary operations and non-increase under local quantum operations and
classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains
Sections 1-5 & 7 of the previous version. The previous Section 6 is now in
quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501
The reduction of the closest disentangled states
We study the closest disentangled state to a given entangled state in any
system (multi-party with any dimension). We obtain the set of equations the
closest disentangled state must satisfy, and show that its reduction is
strongly related to the extremal condition of the local filtering on each
party. Although the equations we obtain are not still tractable, we find some
sufficient conditions for which the closest disentangled state has the same
reduction as the given entangled state. Further, we suggest a prescription to
obtain a tight upper bound of the relative entropy of entanglement in two-qubit
systems.Comment: a crucial error was correcte
High Temperature Macroscopic Entanglement
In this paper I intend to show that macroscopic entanglement is possible at
high temperatures. I analyze multipartite entanglement produced by the
pairing mechanism which features strongly in the fermionic lattice models of
high superconductivity. This problem is shown to be equivalent to
calculating multipartite entanglement in totally symmetric states of qubits. I
demonstrate that we can conclusively calculate the relative entropy of
entanglement within any subset of qubits in an overall symmetric state. Three
main results then follow. First, I show that the condition for
superconductivity, namely the existence of the off diagonal long range order
(ODLRO), is not dependent on two-site entanglement, but on just classical
correlations as the sites become more and more distant. Secondly, the
entanglement that does survive in the thermodynamical limit is the entanglement
of the total lattice and, at half filling, it scales with the log of the number
of sites. It is this entanglement that will exist at temperatures below the
superconducting critical temperature, which can currently be as high as 160
Kelvin. Thirdly, I prove that a complete mixture of symmetric states does not
contain any entanglement in the macroscopic limit. On the other hand, the same
mixture of symmetric states possesses the same two qubit entanglement features
as the pure states involved, in the sense that the mixing does not destroy
entanglement for finite number of qubits, albeit it does decrease it. Maximal
mixing of symmetric states also does not destroy ODLRO and classical
correlations. I discuss various other inequalities between different
entanglements as well as generalizations to the subsystems of any
dimensionality (i.e. higher than spin half).Comment: 14 pages, no figure
Entanglement simulations of Shor's algorithm
We demonstrate that, in the case of Shor's algorithm for factoring, highly
mixed states will allow efficient quantum computation, indeed factorization can
be achieved efficiently with just one initial pure qubit and a supply of
initally maximally mixed qubits (S. Parker and M. B. Plenio, Phys. Rev. Lett.
85, 3049 (2000)) . This leads us to ask how this affects the entanglement in
the algorithm. We thus investigate the behaviour of entanglement in Shor's
algorithm for small numbers of qubits by classical computer simulation of the
quantum computer at different stages of the algorithm. We find that
entanglement is an intrinsic part of the algorithm and that the entanglement
through the algorithm appears to be closely related to the amount of mixing.
Furthermore, if the computer is in a highly mixed state any attempt to remove
entanglement by further mixing of the algorithm results in a significant
decrease in its efficiency.Comment: 17 pages including 16 figures. Typos corrected and more efficient
simulation methods outline
Quantum correlations, local interactions and error correction
We consider the effects of local interactions upon quantum mechanically entangled systems. In particular we demonstrate that non-local correlations cannot increase through local operations on any of the subsystems, but that through the use of quantum error correction methods, correlations can be maintained. We provide two mathematical proofs that local general measurements cannot increase correlations, and also derive general conditions for quantum error correcting codes. Using these we show that local quantum error correction can preserve nonlocal features of entangled quantum systems. We also demonstrate these results by use of specific examples employing correlated optical cavities interacting locally with resonant atoms. By way of counter example, we also describe a mechanism by which correlations can be increased, which demonstrates the need for it non-local interactions
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