quantum entanglement without correlation
DESCRIPTION
presentation from ips 2014TRANSCRIPT
Quantum Entanglement without CorrelationsPresented by Minh TranCo-authors: T. Paterek, L. Knips, W. Laskowski, A. Rosier, C. Schwemmer, H. Weinfurter
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Content
› No-correlation multipartite systems
› Proof of entanglement
› Experimental results.
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Introduction
› Correlated systems
› Example
› Alice measures Bob’s particle is in state .
|Ψ ⟩= 1
√2|0 ⟩ 𝐴⊗|1 ⟩𝐵+
1
√2|1 ⟩ 𝐴⊗|0 ⟩𝐵
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Introduction
› Correlated systems
› All bipartite systems that are entangled are also correlated
› Extrapolation to multipartite systems
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Background: Genuine entanglement
› Different types of entanglement
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Background: Correlation
› Formal definition of correlation
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Construction of no-correlation state
› Construction of anti-state
› Equally mixing state with its anti-state
› Next: Example
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Construction of no-correlation state
› Example:
› Other correlations are or
› Construction of anti-state
› . Other correlations are or
› Mixing state with its anti-state
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Anti-state for odd number of qubits
› General pure state:
› We claim that
has exactly opposite correlations to
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Anti-state for odd number of qubits
› Proof using universal NOT gate
› Here Pauli operators.
› Complex conjugation in the standard basis
› For example
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Anti-state for odd number of qubits
› Action of on
› Proof
𝑁=𝜎𝑧𝜎 𝑥𝐾𝜎 𝑥∨0 ⟩=¿1 ⟩𝜎 𝑥∨1 ⟩=¿0 ⟩𝜎 𝑧∨0 ⟩=¿0 ⟩𝜎 𝑧|1 ⟩=−∨1 ⟩
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Anti-state for odd number of qubits
› Action of universal NOT gate on the Pauli matrices
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Anti-state for odd number of qubits
› Correlations of
for odd n
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Anti-state for odd number of qubits
› We have found the anti state for system of odd number of qubits via NOT gate.
› State with no correlation:
› How about even ?
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Even
› Universal NOT?
› Product state has as its anti-state
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Even
› Even state without anti-state
› Assume this state has an anti-state
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Entanglement of no-correlation states
› For odd consider:
› is genuinely entangled.
› is separable (not entangled)
|𝐺𝐻𝑍 ⟩= 1
√2|00…0 ⟩+ 1
√2|11…1 ⟩
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Entanglement of no-correlation states
› Focus on generalized states:
› For and , this state returns to the usual state.
› Clearly is entangled. Is ?
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Entanglement of W-like states
› Tool: Genuine entanglement witness
› denotes inner product
› is the correlation tensor of a bi-separable state.
› Bi-separable:
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Right hand side
› has the following non-zero correlations:
› Hence independent of
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Left hand side
𝛼
𝛽
Figure 1. Maximum of with different values of . The value is always smaller than 3 except for the trivial cases , in which is always fully separable. In particular, the value of is found to be
is genuinely entangled!
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Argument without plot
› If is bi-separable, there exists a bi-product state
› Assume is bi-product in the cut , then
› Using earlier definition for
› Thus at least one coefficient of must be |Ψ ⟩=sin 𝛽 cos𝛼|100 ⟩+sin 𝛽sin 𝛼|010 ⟩+cos𝛽∨001 ⟩
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Review
› Construction of a family of states with no
multipartite correlations.
› Proof of genuine entanglement in all of the above
states
› Next: Experiment comparison
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Experiment Plot
› Prepare the Dicke state
› Trace out the first qubit
› Measure the correlations
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Experiment’s setup
photons, two , two
Detectora b c
d
H H VV
H V HV
H V VH
V H HV
V H VH
V V HH
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Experiment’s result
Figure 2. Correlations of This state is prepared by projecting the first qubit of the state onto . In this experiment, fidelity of is .
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Experiment’s result
Figure 3. Correlations of This state is prepared by projecting the first qubit of the state onto . In this experiment, fidelity of is .
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Experiment’s result
Figure 4. Correlations of This state is prepared by throwing out the first qubit of the state. In this experiment, fidelity of is .
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Experiment’s result
Figure 5 (Green). Measurement of tripartite correlation. The first qubit was measured by and the other two were measured by .
Note:
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Conclusion
› Construction of a family of states with no
multipartite correlations.
› Proof of genuine entanglement in all of the above
states
› Experiment comparison
› Thank you !