Supremum of Entanglement Measure for Symmetric Gaussian States, and
Entangling Capacity
- URL: http://arxiv.org/abs/2008.03893v2
- Date: Tue, 11 Aug 2020 00:47:15 GMT
- Title: Supremum of Entanglement Measure for Symmetric Gaussian States, and
Entangling Capacity
- Authors: Jhih-Yuan Kao
- Abstract summary: We show a method to calculate bounds for entangling capacity, the amount of entanglement that can be produced by a quantum operation.
We also show the supremum of negativity for symmetric Gaussian states.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this thesis there are two topics: On the entangling capacity, in terms of
negativity, of quantum operations, and on the supremum of negativity for
symmetric Gaussian states.
Positive partial transposition (PPT) states are an important class of states
in quantum information. We show a method to calculate bounds for entangling
capacity, the amount of entanglement that can be produced by a quantum
operation, in terms of negativity, a measure of entanglement. The bounds of
entangling capacity are found to be associated with how non-PPT (PPT
preserving) an operation is. A length that quantifies both entangling
capacity/entanglement and PPT-ness of an operation or state can be defined,
establishing a geometry characterized by PPT-ness. The distance derived from
the length bounds the relative entangling capability, endowing the geometry
with more physical significance.
For a system composed of permutationally symmetric Gaussian modes, by
identifying the boundary of valid states and making necessary change of
variables, the existence and exact value of the supremum of logarithmic
negativity (and negativity likewise) between any two blocks can be shown
analytically. Involving only the total number of interchangeable modes and the
sizes of respective blocks, this result is general and easy to be applied for
such a class of states.
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