Can looping around an exceptional point switch entangled states?
Steering a lossy photonic system around an exceptional point converts one entangled Bell state into another, with the result set by the loop's direction and robust to small errors.
Source
Topologically protected entanglement switching around exceptional points
Study at a glance
- Design
- Other — Non-Hermitian quantum walk theory with a two-photon polarisation experiment reconstructed by quantum state tomography
- N
- No sample N; the experiment used an 8-step quantum walk with four Bell-state inputs, two encircling directions, and ten random disorder realisations
- Population
- Polarisation-entangled photon pairs from type-I down-conversion in a BBO crystal
- Outcome
- Fidelity of output states to target Bell states and theory-experiment similarity
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What they did
The authors designed a non-Hermitian quantum walk with gain-loss operators whose eigenstates closely match the four Bell states and share a four-fold exceptional point. They varied two parameters in a loop around the point, clockwise or counterclockwise, first in theory with 100 steps and then experimentally with polarisation-entangled photon pairs using wave plates and partially polarising beam splitters. Output states were reconstructed by two-photon tomography, and robustness was tested by adding random wave-plate angle errors.
What they found
In theory, a clockwise loop sent two Bell states to the same output and a counterclockwise loop sent them to the partner state, with fidelities up to 98.3%. In the 8-step experiment all output fidelities to ideal Bell states were at least 84%, and theory-experiment similarity exceeded 92%. A loop that did not enclose the exceptional point lost the chiral behaviour, and random angle disorder barely changed the fidelities, which stayed above 0.8.
The limits
What it doesn't show
The experiment only used 8 steps because photon loss makes long walks hard, so it approximates rather than fully meets the adiabatic condition, and fidelities are lower than in theory. Gain and loss are simulated by relative loss in passive optics, so the system is not a truly amplifying one, and the lost photons are a source of error. Robustness was tested only against small angle disorder, not against other realistic noise such as decoherence in a larger network. Whether this scales to more qubits is not shown.
Key terms
- Exceptional point
- A degeneracy in a non-Hermitian system where both eigenvalues and eigenvectors coalesce.
- Bell state
- One of four maximally entangled two-qubit states.
- Non-Hermitian system
- A system with gain or loss whose evolution is not unitary, so probability is not conserved.
- Quantum walk
- A quantum analogue of a random walk built from repeated rotation and conditional shift operations.
- Fidelity
- A 0-to-1 measure of how close a measured quantum state is to a target state.
- Chiral state conversion
- An asymmetric switching where the final state depends on the direction the parameter loop is traversed.
Flashcards
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Quiz yourself
What determines which Bell state is produced after encircling the exceptional point?
Common questions
Why does the direction around the exceptional point matter?
Along one direction the state starts on a gain branch and follows it adiabatically, while the other direction starts on a loss branch where tiny nonadiabatic jumps send it back to the gain branch, so the outputs differ.
What makes the operation topologically protected?
The outcome depends on whether the loop encloses the exceptional point, not on the precise path, so small parameter errors do not change it.
Why did the experiment use only 8 steps?
Each step loses photons; the authors found that unequally spaced parameters let 8 steps approximate the 100-step result.
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