distillation and determination of unknown two-qubit entanglement:
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ESF conference: Quantum Engineering of States and Devices June 9, 2010, Obergurgl. Distillation and determination of unknown two-qubit entanglement: Construction of optimal witness operator. Heung-Sun Sim Physics, KAIST. (theory) S.-S. B. Lee and H.-S. Sim, PRA 79, 052336 (2009) - PowerPoint PPT PresentationTRANSCRIPT
Distillation and determination of
unknown two-qubit entanglement:
Construction of optimal witness operator
Heung-Sun Sim
Physics, KAIST
ESF conference: Quantum Engineering of States and
DevicesJune 9, 2010, Obergurgl
(theory) S.-S. B. Lee and H.-S. Sim, PRA 79, 052336 (2009)(theory + experiment) H. S. Park, S.-S. B. Lee, H. Kim, S.-K. Choi, and H.-S. Sim, arXiv:1006.1491 (2010)
Acknowledgement: S.-S. B. Lee (KAIST), H. S. Park, H. Kim, S.-K. Choi (KRISS)
Outline IA two-qubit interferometer:
• Local filtering operations (SLOCC) to focus on entanglement (Procrustean
distillation)
• Two-qubit correlation to construct the optimal entanglement witness
Outline II
Iterative distillation and quantification
A new scheme for detecting, distilling, and quantifying two-qubit entanglement without full state reconstruction.
• The exact value of concurrence is determined. Always successful.
• Better efficiency than quantum state tomography
• Experimental demonstration with photons
• Extendible to multiqubit cases, qubits in condensed matter
Entanglement detection and quantifcation
Detecting or quantifying entanglement? Separability criteria Entanglement measures Two-qubit entanglement: Concurrence
Pure state CH Bennett et al PRA 54, 3824 (1996)
Example
Concurrence
Mixed state: convex roof extensionAlgebraic expression is available!
WK Wootters PRL 80, 2245 (1998)
Entanglement detection and quantifcation in experiments
1. Tomography + mathematical criteria- Do state tomography and apply criterion or concurrence
formula.- Weakness: Full state reconstruction. Indirect.
Impractical in multiqubit cases.- Most efficient way so far.
2. Bell inequality- Classical concept. Violation means entanglement.- Weakness: Not always successful. Not quantitative.
3. Entanglement witness- Physical observable. Negative expectation values mean
entanglement.- Weakness: Not always successful. Not quantitative.
Questions:- Quantification without tomography?- Measuring entanglement measure?
Nonlinear functions of density matrix…
- Two-qubit experiments with two state copiesS. P. Walborn et al., Nature
(2006)
Our goal:
Construct the optimal witnesswithout referring the full knowledge of the target state
Modification of a two-qubit interferometry is necessary!
two-qubit interferometry in quantum optics
two-qubit interferometry in condensed matter
multi-qubit GHZ interferometry in condensed matter
Theory: P Samuelsson, EV Sukhorukov, M Buttker, PRL (2004)
Experiment: I. Neder et al., Nature (2007)
Theory: HS Sim, EV Sukhorukov, PRL (2006)
Optimal entanglement witness
Optimal witness Physical observable useful for entanglement
quantification Defined relative to a given state
Expectation value gives concurrence
Graphical interpretation
Procrustean distillationProcrustean distillation Enhance entanglement via SLOCC (stochastic local
operation and classical communication)
Example: Stochastic local filtering of qubit 1 when qubit 1 is downspin.
Link to the optimal witness
PG Kwiat et al., Nature (2001)
Our setup How to attach the filtering operation into the
interferometry?f<1
Using beam splitter(or quantum point contact in
quantum Hall interferometry)
How to achieve the maximal distillation Maximal distillation = Fully mixed local density matrices Iteratively erase single-qubit interference until it vanishes
This procedure does not require full state reconstruction
How to construct the optimal witness Measure two-qubit correlation (coincidence counting)
Three different pairs of local extrema of
First find the settings for measuring and then measure
Not require tomography, More efficient than tomographyS.-S. B. Lee and H.-S. Sim, PRA 79, 052336 (2009)
Experimental demonstration
H. S. Park, S.-S. B. Lee, H. Kim, S.-K. Choi, and H.-S. Sim, preprint (2010)
Summary Determination of concurrence without quantum state
tomography
The first construction of the optimal witness operator
Entanglement distillation and quantification within a single framework
Generic scheme for photons, electrons, …
Extendible to three-qubit Greenberger-Horne-Zeilinger entanglement
Thank you for your attention!
(theory) S.-S. B. Lee and H.-S. Sim, PRA 79, 052336 (2009)(theory + experiment) H. S. Park, S.-S. B. Lee, H. Kim, S.-K. Choi, and H.-S. Sim, arXiv:1006.1491 (2010)