Time-bin coding

Time-bin coding (Engl. Time-bin-encoding , TBE) is in the quantum computer science a way to a qubit on a photon to encode . The main area of ​​application is quantum cryptography .

General properties

Qubits are any two-level quantum mechanical systems. Qubits can be represented in various physical implementations, one of which is the TBE. The technology of the TBE is extremely robust against decoherence . However, it does not allow (simple) interaction between the various qubits. This property in particular predestines the TBE for use in quantum communication.

The TBE is the quantum mechanical extension of the Mach-Zehnder modulator .

A possible setup of the time-bin coding with fiber optic MZI. At the beginning of the interferometer there is a laser diode (LD), and at the end there are two detectors of the avalanche photodiode (APD) type, one APD each for recording the bases and . ${\displaystyle |0\rangle }$ ${\displaystyle |1\rangle }$

implementation

The simplest setup for performing the coding consists of a Mach-Zehnder interferometer (MZI) through which a single photon is passed. The MZI can be made from elements of fiber optics and / or free space optical components.

The incoming photon has the option of using two paths of different lengths. It is important that the difference in path length is longer than the coherence length of the photon. This ensures that the path used can be clearly identified. Furthermore, the phase stability of the interferometer must be extremely good. In practice, this means that a possible change in the path length difference between the two paths during the photon transfer may be much less than the wavelength of the photon used. Therefore, TBE requires, among other things, an active temperature stabilization.

Mathematical-physical description

If the photon takes the short path, then it is determined that this corresponds to the state . If the long way is used, the condition is there. If the probability of choosing one of the two paths is different from zero, then there is a coherent superposition of the two states. ${\displaystyle |0\rangle }$ ${\displaystyle |1\rangle }$

${\displaystyle |\psi \rangle =\alpha \cdot |0\rangle +\beta \cdot |1\rangle }$

With:

${\displaystyle \alpha ^{2}+\beta ^{2}=1}$

This coherent superposition is the qubit as a fundamental component of quantum computing. ${\displaystyle |\psi \rangle }$

There is now the possibility of actively influencing the phase . In the fiber optic setup, for example, using a fiber stretcher or a built - in electro-optic modulator (EOM). The amplitude of the photon can also be manipulated in a targeted manner. The latter option is much more difficult to implement. In general, it is therefore specified that the amplitudes should be evenly distributed in the various paths, i.e. 50:50. The then created, phase-manipulated qubit can be described by: ${\displaystyle \varphi }$

${\displaystyle |\psi \rangle ={|0\rangle +e^{-i\cdot \varphi }\cdot |1\rangle \over {\sqrt {2}}}}$

Measurement

A measurement on the basis of the bases now available takes place via the arrival time of the photon. Measurement with other, additional bases can be achieved by letting the photon pass through another MZI. If both interferometers are identical (except ), one speaks of a time-bin configuration (English time-bin implementation). ${\displaystyle \{|0\rangle ,|1\rangle \}}$ ${\displaystyle \varphi }$

The subset of the qubit measurements possible in each case is small. The generation of the state and the measurement setup considerably limit the number of qubit representations.

literature

• Nicolas Gisin, Grégoire Ribordy, Wolfgang Tittel, Hugo Zbinden: Quantum Cryptography . PDF accessed on March 20, 2018 (English)
• Matthias Leifgen: Protocols and components for quantum key distribution . PDF accessed on March 20, 2018 (English)
• Björnstjerne Zindler: Construction of fiber-based interferometers for quantum cryptography . PDF accessed on March 20, 2018 (German) (2.363 MB)

Individual evidence

1. ↑ Jeongwan Jin, Sascha Agne, Jean-Philippe Bourgoin, Yanbao Zhang, Norbert Lütkenhaus and Thomas Jennewein: Efficient time-bin qubit analyzer compatible with multimode optical channels. Quantum Physics, September 25, 2015, accessed March 26, 2018 . 
2. ^ Todd Pittman: It's a Good Time for Time-Bin Qubits. Physical Review, October 9, 2013, accessed March 26, 2018 . 
3. ↑ Matthias Leifgen: Chapter 7.1.1.1 Requirements for the interferometer . In: Protocols and Components for Quantum Key Distribution . 2016, doi : 10.18452 / 17473 .
4. ↑ Matthias Leifgen: Chapter 7.1.1.2 Experimental implementation of the interferometer . In: Protocols and Components for Quantum Key Distribution . 2016, doi : 10.18452 / 17473 .
5. ↑ Björnstjerne Zindler: Chapter 2.1 + 2.2 Modules of the Time-Bin configuration . In: Structure of fiber-based interferometers for quantum cryptography . 2011 ( nadirpoint.de [PDF]).
6. ↑ Matthias Leifgen: Chapter 4.2 The time-bin implementation . In: Protocols and Components for Quantum Key Distribution . 2016, doi : 10.18452 / 17473 .