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Distinguishability of Hyper-
entangled Bell states
Neal PisentiProfessor Theresa Lynn (Advisor)
Physics Department, Harvey Mudd College
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Teleportation in SyFy?
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Teleportation in SyFy?
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Bell-State
Measurement
What can go wrong in
quantum teleportation?
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What could go wrong?
We aren't able to make a completeBell-state measurement!!
My thesis: What is the upper bound on
Bell-statedistinguishability using linear evolution, local
measurement devices?
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Entanglement
When two particles know their relationship to each
other better than they know their own states...
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Entanglement variables...
Spins of an electron?
Polarization states of a photon?
discrete linear momentum states,pairs of orbital angular
momentum states, orANY two-level system!
?
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4 Bell states for each variable
thus...
4n hyper-entangledBell states in n variables!
Hyper-entangled Bell states?
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Bell-State
Measurement
What can go wrong in
quantum teleportation?
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2n+1 single-particleinput states
2n+1 single-detectoroutput states
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2n+1 single-particleinput states
2n+1 single-detectoroutput states
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Bell-state distinguishability comes
from the seconddetector firing!
Hence, there can be at most 2n+1 distinguishablemeasurement
classes, one for each second-detector
event.
But, forn = 1 and n = 2, shown computationally that thereare
really only 2n+1 - 1 classes.
Does this hold for larger values ofn ??
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How about looking for some
symmetries?
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Let's propose some hypothetical detectionsignature that is
anti-symmetric with this:
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0
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Two possible cases:
is a single detector, say, detector
OR
is some superposition of detectors.
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Two possible cases:
is a single detector, say, detector
0
If detectori fires, detectorjwill not fire.
Thus, there are fewer than 2n+1 possibilities for the
seconddetector event, and the best we can do is...
2n+1
- 1 distinguishable Bell-state classes!
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Two possible cases:
is some superposition of detectors.
... 0
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Results
Proved for general n that we can only distinguish between
2n+1 - 1 Bell states out of 4n total.
Provided a new, intuitive understanding of the
distinguishabilitylimits based on symmetries in the detection
signatures.
Also proved that there is a minimum Bell-state class size for
anygiven detection signature:
No fewer than 2n Bell states if a detector fires twice.No fewer
than 2n-1 Bell states if two distinct detectors fire.
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Acknowledgements
Professor Theresa Lynn Comrades-in-arms:
o DK, Greg, Julien, Robert Dmitri Skjorshammer
Professor Orrison Philipp Gaebler
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Questions?
