Quantum entanglement without correlation

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 !