entanglement witnesses for hybrid systems
TRANSCRIPT
ENTANGLEMENT
Witnessing
in hybrid systems
“I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.”
Entanglement is a resource
?NP hard
ENTANGLEMENT
Witnessing
Hermitian operator
detects entanglement of if
for any separable state
3 Examples
1
2
3
2 criteria
C2 Use of local measurements
Assumption on the form of the microscopic Hamiltonian and/or the Hilbert space of the system
C1
1
Up to 6 entangled qubits
C1
C2
C2
CROSSTALK
C1
C2
C1
C2
PROBLEM WITH C1 and C2
Quantum simulationsManybody systems
ENTANGLEMENT
Global Witnesses of
P. Krammer et al. “Multipartite Entanglement Detection via Structure Factors”, PRL 103, 100502 (2009)
Structure factor
M. Cramer et al. “Measuring Entanglement in Condensed Matter Systems”, PRL 106, 020401 (2011)
Structure factor
ri rj
light/neutrons
scattered light/neutrons
Witness
Structure factors
Witness
C2
C1Independent of the form of the microscopic Hamiltonian
Requires only global measurements
Great!
Experiments
Experiments
Trapped ionsBragg scattering
Pump-probe experiment
PROBED
⌦1 ⌦0
PUMP LASER PAIR
C. Macchiavello and G. Morigi “Entanglement detection via Bragg scattering”, PRA 87, 044301 (2013)
What if the positions are quantized ?
Q Witnessfor Trapped ions
position operatorsquantized motion
How does a quantum environment affect spin entanglement detection by ?
Can we define a generalised witness and use it to detect entanglement in hybrid systems ?
ENTANGLEMENT
Witnessing
in hybrid systemsMassimo Borrelli, Matteo Rossi, Chiara Macchiavello, S.M.
arXiv:1404.6083
Q Witness
?
Q Witnessfor Trapped ions
N spins factorised state collective vibrational state
For
Q Witnessfor Trapped ions
normal modes decomposition
How does a quantum environment affect spin entanglement detection by ?
Q Witnessfor Trapped ions
sinusoidal modulation of the collective vibrational state characteristic function
if
Q Witnessfor Trapped ions
Example 1
One collective vibrational mode in a thermal state
2 effective spins
Optimal Q Witness
for Trapped ions
cx
= 1, cy
= 1, cz
= �1
Optimal Q Witness
q’
� = ~⌫/kBT
� = 100low T
� = 1
� = 100
low T
high T
Can we define a generalised witness and use it to detect entanglement in hybrid systems ?
Q Witnessfor Trapped ions
Example 2 2 spins
One collective vibrational mode
state 1
↵ = 1↵ = 0
state 2
state 3
Optimal Q Witness
q’
↵ = 0
Optimal Q Witness
q’
↵ = 1
Optimal Q Witness
q’
|↵| > 1? ?
Optimal Q Witness
q’
Optimal Q Witness
q’
hybrid entanglement
short summary
spin detection:the cooler the better!
spin detection:shit happens!
witnessing hybrid entanglement!
what next ?
ENTANGLEMENT
Witnessing
in hybrid systems
Hybrid entanglement witness
what next ?
ENTANGLEMENT
Witnessing
in hybrid systems
...one more minute ???
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