physics

Time-bin encoding

Time-bin encoding is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Time-bin encoding rather than just read about it. In short: Time-bin encoding is a technique used in quantum information science to encode a qubit of information on a photon. Quantum information science makes use of qubits as a basic resource similar to bits in classical computing.

Key takeaways

Time-bin encoding belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Time-bin encoding to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Time-bin encoding from memory before moving on to harder problems.

Reference excerpt

Time-bin encoding is a technique used in quantum information science to encode a qubit of information on a photon. Quantum information science makes use of qubits as a basic resource similar to bits in classical computing. Qubits are any two-level quantum mechanical system; there are many different physical implementations of qubits, one of which is time-bin encoding. While the time-bin encoding technique is very robust against decoherence, it does not allow easy interaction between the different qubits. As such, it is much more useful in quantum communication (such as quantum teleportation and quantum key distribution) than in quantum computation.

Construction of a time-bin encoded qubit

Time-bin encoding is done by having a single-photon go through a Mach–Zehnder interferometer (MZ), shown in black here. The photon coming from the left is guided through one of two paths (shown in blue and red); the guiding can be made by optical fiber or simply in free space using mirrors and polarising cubes. One of the two paths is longer than the other. The difference in path length must be longer than the coherence length of the photon to make sure the path taken can be unambiguously distinguished. The interferometer has to keep a stable phase, which means that the path length difference must vary by much less than the wavelength of light during the experiment. This usually requires active temperature stabilization. If the photon takes the short path, it is said to be in the state | 0 ⟩ {\displaystyle |0\rangle } ; if it takes the long path, it is said to be in the state | 1 ⟩ {\displaystyle |1\rangle } . If the photon has a non-zero probability to take either path, then it is in a coherent superposition of the two states:

| ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ , {\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle ,}

These coherent superpositions of the two possible states are called qubits, which are the basic ingredient of Quantum information science. In general, it is easy to vary the phase gained by the photon between the two paths, for example by stretching the fiber, while it is much more difficult to vary the amplitudes which are therefore fixed, typically at 50%. The created qubit is then

| ψ ⟩ = | 0 ⟩ + e i ϕ | 1 ⟩ 2 , {\displaystyle |\psi \rangle ={\frac {|0\rangle +e^{i\phi }|1\rangle }{\sqrt {2}}},}

which covers only a subset of all possible qubits. Measurement in the { | 0 ⟩ , | 1 ⟩ } {\displaystyle \{|0\rangle ,|1\rangle \}} basis is done by measuring the time of arrival of the photon. Measurement in other bases can be achieved by letting the photon go through a second MZ before measurement, though similar to the state preparation, the possible measurement setups are restricted to only a small subset of possible qubit measurements.

Decoherence Time-bin qubits do not suffer from depolarization or polarization mode-dispersion, making them better suited to fiber optics applications than polarization encoding. Photon loss is easily detectable since the absence of photons does not correspond to an allowed state, making it better suited than a photon-number based encoding.

References Marcikic, I.; De Riedmatten, H.; Tittel, W.; Scarani, V.; Zbinden, H.; Gisin, N. (2002). "Time-bin entangled qubits for quantum communication created by femtosecond pulses". Physical Review A. 66 (6) 062308. arXiv:quant-ph/0205144. Bibcode:2002PhRvA..66f2308M. doi:10.1103/PhysRevA.66.062308. S2CID 118932433. Donohue, John M.; Agnew, Megan; Lavoie, Jonathan; Resch, Kevin J. (2013). "Coherent Ultrafast Measurement of Time-Bin Encoded Photons". Physical Review Letters. 111 (15) 153602. arXiv:1306.1250. Bibcode:2013PhRvL.111o3602D. doi:10.1103/PhysRevLett.111.153602. PMID 24160599. S2CID 42286193. Martin, A.; Kaiser, F.; Vernier, A.; Beveratos, A.; Scarani, V.; Tanzilli, S. (2013). "Cross time-bin photonic entanglement for quantum key distribution". Physical Review A. 87 (2) 020301. arXiv:1207.6586. Bibcode:2013PhRvA..87b0301M. doi:10.1103/PhysRevA.87.020301. S2CID 11312035. Marcikic, I.; De Riedmatten, H.; Tittel, W.; Zbinden, H.; Legré, M.; Gisin, N. (2004). "Distribution of Time-Bin Entangled Qubits over 50 km of Optical Fiber". Physical Review Letters. 93 (18) 180502. arXiv:quant-ph/0404124. Bibcode:2004PhRvL..93r0502M. doi:10.1103/PhysRevLett.93.180502. PMID 15525142. S2CID 13120600. Pittman, Todd (2013). "It's a Good Time for Time-Bin Qubits". Physics. 6: 110. Bibcode:2013PhyOJ...6..110P. doi:10.1103/Physics.6.110. hdl:11603/19318. Gündoǧan, Mustafa; Ledingham, Patrick M.; Kutluer, Kutlu; Mazzera, Margherita; De Riedmatten, Hugues (2015). "Solid State Spin-Wave Quantum Memory for Time-Bin Qubits". Physical Review Letters. 114 (23) 230501. arXiv:1501.03980. Bibcode:2015PhRvL.114w0501G. doi:10.1103/PhysRevLett.114.230501. PMID 26196784. S2CID 17555337.

Worked examples

Example 1 — a first encounter with Time-bin encoding

Start with the simplest possible case. Write down what Time-bin encoding claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Time-bin encoding before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Time-bin encoding ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Time-bin encoding

In research: Time-bin encoding appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Time-bin encoding in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Time-bin encoding is common in secondary-school and first-year university syllabi. It links to neighbouring topics Quantum information science, so understanding it makes those chapters shorter.
In everyday life: Look for Time-bin encoding outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Time-bin encoding in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Time-bin encoding means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Time-bin encoding out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Time-bin encoding in simple terms?

Why does Time-bin encoding matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Time-bin encoding?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Time-bin encoding.