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Measuring Multi-particle Entanglement

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Matthew Leifer
Matthew Leifer

Talk circa 2003 based on the results of Physical Review A 69, 052304 (2004) (also available at http://arxiv.org/abs/quant-ph/0308008)

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Measuring Multi-particle Entanglement M. S. Leifer, N. Linden, A. Winter University of Bristol RESQ Workshop - Jan. 2003
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
1) Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
1) Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2) Invariants Orbits under action of for some = canonical point Equivalence under local unitary transformations ,[object Object],[object Object],[object Object]
2) Invariants Definition - is an invariant function under LU transformations if ,[object Object],[object Object],These are single copy invariants. Similarly for mixed states under: (pure states) (mixed states) At least i.e. almost all!
3) Measuring Invariants Measure Pre- processing The polynomial invariants can be written in this form
4) Polynomial Invariants Invariants under Consider acting on 1 independent invariant - is the invariant tensor. Under - invariant tensors ? Products of ’s acting on different particles. Construct invariants by contracting with .
4) Polynomial Invariants Example: Two-qudits Quadratic: Quartic:
4) Polynomial Invariants ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
5) SLOCC Invariants ,[object Object],[object Object],[object Object],[object Object],[object Object]
5) SLOCC Invariants ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
5) SLOCC Invariants Transpose - not physical! If it were - General Protocol for  invariants. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The SPA ,[object Object], = +ve, but not completely +ve map. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
6) Evaluation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
7) Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Measuring Multi-particle Entanglement

  • 1. Measuring Multi-particle Entanglement M. S. Leifer, N. Linden, A. Winter University of Bristol RESQ Workshop - Jan. 2003
  • 2.
  • 3.
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  • 7. 3) Measuring Invariants Measure Pre- processing The polynomial invariants can be written in this form
  • 8. 4) Polynomial Invariants Invariants under Consider acting on 1 independent invariant - is the invariant tensor. Under - invariant tensors ? Products of ’s acting on different particles. Construct invariants by contracting with .
  • 9. 4) Polynomial Invariants Example: Two-qudits Quadratic: Quartic:
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