Polarization Photonic Qubit

Figure

Description

A polarization photonic qubit encodes a two-level state in orthogonal polarization modes of one photon,

$|\psi ⟩=\alpha |H⟩+\beta e^{i\varphi }|V⟩.$

Waveplates or integrated birefringent elements implement arbitrary single-qubit rotations, while polarizing beam splitters provide state analysis. Polarization is the most direct free-space photonic encoding and is ubiquitous in entanglement distribution and quantum communication. Its principal weakness is uncontrolled birefringence in fibres and integrated waveguides; time-bin and frequency-bin encodings often travel more robustly.

Hamiltonian and Control

Any lossless polarization transformation is an $SU(2)$ rotation,

$U(\theta ,\mathbf{n})=\exp \left(-i\frac{\theta }{2}\mathbf{n}\cdot \mathbf{\sigma }\right),$

implemented optically with retarders or polarization-preserving integrated circuits. Two-photon entangling gates are usually measurement-induced: Hong-Ou-Mandel interference plus polarization-dependent beam splitting realizes a nondeterministic CNOT.

Motivation

• Encode a qubit in a degree of freedom that is simple to prepare, transform, and measure.
• Interface naturally with entangled-photon sources, quantum memories, and free-space links.
• Avoid path duplication for many single-qubit operations.

Experimental Status

Polarization qubits are a mature quantum-communication encoding. Crespi et al. demonstrated the first integrated polarization-encoded CNOT in 2011 using laser-written partially polarizing directional couplers, with logical-basis fidelity $0.940\pm 0.004$ and process fidelity $0.906\pm 0.003$.

Key Metrics

Metric	Value	Notes	Fidelity reference
CNOT truth-table fidelity	0.940 ± 0.004	Integrated polarization gate	Crespi et al. 2011
CNOT process fidelity	0.906 ± 0.003	Quantum process tomography	Crespi et al. 2011
Bell-state discrimination probability	0.877 ± 0.007	Same integrated device	Crespi et al. 2011

Scaling Considerations

• Fibre birefringence and polarization-mode dispersion demand active compensation.
• Integrated circuits must preserve both polarization modes with matched loss and phase.
• Deterministic photon-photon interactions remain absent; scalable computing relies on ancillas, feed-forward, cluster states, or fusion.

References

• A. Crespi et al., “Integrated photonic quantum gates for polarization qubits,” Nature Communications 2, 566 (2011).

Linked Papers

• crespi-2011-polarization-photonic-gates

Evergreen context

• erasure-error-vs-pauli-error — photon loss is often detectable and should not be modeled as an anonymous Pauli error.
• threshold-theorem — explains why probabilistic gates require architectural overhead rather than invalidating scalability outright.

Related Entries

• time-bin-photonic-qubit — more robust for long fibre links.
• dual-rail-photonic-qubit — path-mode encoding favored in integrated LOQC.
• frequency-bin-photonic-qubit — spectral-mode encoding compatible with electro-optic processing.