Time-Bin Photonic Qubit

Figure

Description

The time-bin qubit encodes quantum information in the temporal degree of freedom of a single photon: $|0⟩\equiv |\text{early}⟩$ and $|1⟩\equiv |\text{late}⟩$, corresponding to two well-separated time slots (typically $\Delta t\sim 1-5\text{ns}$) within a single optical pulse window. Superposition states $\alpha |\text{early}⟩+\beta |\text{late}⟩$ are prepared by passing a single photon through an unbalanced Mach-Zehnder interferometer, where the path-length difference defines the time-bin separation.

Time-bin encoding is the natural choice for fiber-based quantum communication because it is inherently robust against polarization-mode dispersion and birefringence fluctuations in optical fibers — the dominant decoherence mechanisms that plague polarization-encoded photonic qubits over long distances. The two time bins experience identical polarization transformations in the fiber (assuming slow polarization drift compared to $\Delta t$), making the encoding self-compensating.

Measurement in the computational basis requires only time-resolved single-photon detection, while measurement in the superposition basis uses a second unbalanced interferometer matched to the preparation interferometer. This encoding was introduced by Brendel et al. (1999) and has become the standard for long-distance quantum key distribution and quantum teleportation experiments over deployed fiber networks.

Hamiltonian

The time-bin qubit is described by the single-photon state in a two-mode temporal basis:

$|\psi ⟩=\alpha {\hat{a}}_E^{†}|0⟩+\beta {\hat{a}}_L^{†}|0⟩$

where ${\hat{a}}_E^{†}$ and ${\hat{a}}_L^{†}$ create a photon in the early and late time bins, respectively.

The unbalanced Mach-Zehnder interferometer implements the beam-splitter transformation:

$U_{\text{MZI}}=\left(\begin{array}{cc}\cos \theta & e^{i\varphi }\sin \theta \\ -e^{-i\varphi }\sin \theta & \cos \theta \end{array}\right)$

where $\theta$ is set by the beam-splitter ratio and $\varphi$ is the relative phase between the two arms. A balanced beam splitter ($\theta =\pi /4$) with phase $\varphi$ prepares:

$|\psi ⟩=\frac{1}{\sqrt{2}}(|\text{early}⟩+e^{i\varphi }|\text{late}⟩)$

Motivation

Polarization qubits suffer rapid decoherence in optical fibers due to birefringence, polarization-mode dispersion, and mechanical stress — effects that fluctuate unpredictably over km-scale links. Time-bin encoding eliminates these issues because both temporal modes traverse the same fiber path and experience identical polarization evolution. This makes time-bin qubits the preferred encoding for deployed fiber-based quantum networks, QKD systems, and long-distance quantum teleportation, where stability over hours to days is required without active polarization compensation.

Experimental Status

First demonstration — Brendel et al. (1999):

• Introduced time-bin encoding and demonstrated pulsed energy-time entangled twin-photon source
• Franson interferometry using time-bin entangled photon pairs demonstrated violation of Bell inequalities

Fiber teleportation — Marcikic et al. (2004):

• Distribution of time-bin entangled qubits over 50 km of optical fiber at telecom wavelengths
• Established viability of time-bin encoding for long-distance quantum communication

Long-distance distribution — Takesue et al. (2015):

• Quantum teleportation over 100 km of fiber using highly efficient superconducting nanowire single-photon detectors
• Time-bin encoding at 1550 nm telecom wavelength

Commercial deployment:

• Time-bin encoding adopted in commercial QKD systems (ID Quantique, Toshiba) operating over 100+ km fiber links
• Compatible with integrated photonic circuits: on-chip time-bin sources and interferometers demonstrated in silicon photonics

Key Metrics

Metric	Value	Notes	Fidelity reference
Time-bin separation	1–5 ns	Set by interferometer path difference	Brendel et al. 1999
Fiber transmission distance	>100 km	At telecom wavelengths (1550 nm)	Takesue et al. 2015
State preparation fidelity	>99%	Interferometric visibility	Marcikic et al. 2004
Bell-state visibility	>95%	Franson interferometry	Brendel et al. 1999
Photon loss rate	~0.2 dB/km	Standard telecom fiber at 1550 nm	—
Detector timing jitter	<100 ps	Superconducting nanowire SPDs	—
Operating temperature	300 K (fiber) / 1 K (detectors)	SNSPDs require cryogenics	—

References

Original proposal

• J. Brendel et al., “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82, 2594 (1999)

Experimental demonstrations

• I. Marcikic et al., “Distribution of Time-Bin Entangled Qubits over 50 km of Optical Fiber,” Phys. Rev. Lett. 93, 180502 (2004)
• H. Takesue et al., “Quantum teleportation over 100 km of fiber using highly efficient superconducting nanowire single-photon detectors,” Optica 2, 832 (2015)

Linked Papers

• brendel-1999-time-bin-entanglement
• marcikic-2004-teleportation-fiber

Related Entries

• dual-rail-photonic-qubit — alternative photonic encoding using spatial modes
• fusion-based-photonic-qubit — photonic architecture compatible with time-bin encoding
• coherence-time-hierarchy — context for comparing decoherence mechanisms