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Analysis of polarization mode dispersion effect on quantum state decoherence in fiber-based optical quantum communication
Abstract
The implementation of quantum communication protocols in long optical fibers is limited by several decoherence mechanisms. In this contribution we review this mechanisms and analysis their effect on the quantum states. Because of asymmetry in the real fibers, the two orthogonal polarization modes are propagated at different phase and group velocities. The difference in group velocities results in Polarization Mode Dispersion (PMD). It is created by random fluctuations of the residual birefringence in optical fibers, such that the State of Polarization (SOP) of an optical signal will turn randomly over time, in an unpredictable way. In optical quantum communication, quantum state measurement is necessary. The bottleneck for communication between far apart nodes is the increasing of the error probability with the length of the channel connecting the nodes. For an optical fiber, the value of absorption and depolarization of a photon (i.e., the qubit) increases exponentially with the length of the fiber.
... , where is the base frequency, and n = 0,1,2 … . Energy levels (48) are equally-spaced. In my model, similar pattern is exhibited by energy levels of statistical ensemble of cardinality = 3, as shown on Figure 1. ...
... The combined energy levels are thus given by (51). I can use (48) as approximation for the combined energy levels (51) in expression for partition function (65) with degeneracy of each level = !=6, and obtain the mean energy of modes for subsystems with given as [28]: ...
... In my model, the notion of a photon is meaningless. The quantized energy levels (9,48,51) make transitions between modes appear as absorption or emission of particles. ...
... , where is the base frequency, and n = 0,1,2 … . Energy levels (48) are equally-spaced. In my model, similar pattern is exhibited by energy levels of statistical ensemble of cardinality = 3, as shown on Figure 1. ...
... The combined energy levels are thus given by (51). I can use (48) as approximation for the combined energy levels (51) in expression for partition function (65) with degeneracy of each level = !=6, and obtain the mean energy of modes for subsystems with given as [28]: ...
... In my model, the notion of a photon is meaningless. The quantized energy levels (9,48,51) make transitions between modes appear as absorption or emission of particles. ...
I propose a model wherein a system is represented by a finite sequence of natural numbers. These numbers are thought of as population numbers in statistical ensemble formed as a sample with replacement of entities (microstates) from some abstract set. I derive the concepts of energy and of temperature. I show an analogy between energy spectra computed from the model and energy spectra of some known constructs, such as particle in a box and quantum harmonic oscillator. The presented model replaces the concept of wave function with knowledge vector. I derive Schrödinger-type equation for knowledge vector and discuss principal differences with Schrödinger equation. The model retains major QM hallmarks such as wave-particle duality, violation of Bell’s inequalities, quantum Zeno effect, uncertainty relations, while avoiding controversial concept of wave function collapse. Unlike standard QM and Newtonian mechanics, the presented model has the Second Law of Thermodynamics built-in; in particular, it is not invariant with respect to time reversal.
... A is a dimensionless parameter characterizing the strength of the coupling between the polarization and the "external" environment at temperature T. Next, when thermal noise is ignored and only the birefringence effect is considered, we can obtain the mean square DGD of the fiber ⟨︁ τ 2 ⟩︁ , which can be defined as the group-delay difference between the slow and fast polarization modes |0⟩, |1⟩ as follows [26] ⟨︁ ...
We investigate the effects of polarization mode dispersion (PMD) on the propagation of single- and two-photon states in single-mode fibers. We look at PMD as decoherence due to the system's coupling with the bosonic environment involved in optical birefringence and a thermal bath, respectively. The evolution of the polarization density matrix is described by a master equation, and its solution is used to calculate the differential group delay (DGD) due to the fiber. The PMD effects on the dynamics of EPR states in optical fibers are investigated by using the same method. In both the short-time and long-time regimes, we find that PMD-induced and thermal-induced decoherence behave similarly.
... 1. Rayleigh scattering [12,13] 2. Brownian motion [14,15] 3. Dispersive media [16,17] 4. Recombination of electron-hole pairs in semiconductors [18] It is not in the scope of this paper to consider de-coherence mechanisms in detail. Rather, I shall pursue a generic approach. ...
We address the propagation of entanglement in fibers and investigate the decoherence of polarization-entangled photon pairs caused by polarization mode dispersion (PMD). We devise a decoherence model starting from the statistical properties of polarization mode dispersion and obtain the density matrix describing initially maximally entangled states at any time. Using these results, we derive how decoherence depends on the length of the fibers. We calculate the mean concurrence of the entangled states with PMD effects as a function of fiber length, bandwidth, and other parameters in different cases.
I suggest an object acted on by classical (i.e. non-coherent) force, in gravitational field, unavoidably decays. I estimate decay rates in some scenarios.
We present a quantum key distribution scheme, based on polarization encoding, that is robust against collective noise by sending orthogonal polarization modes of each photon through different channels and postselection. It has lower bit error rate and only needs local polarization measurement. Compare with similar schemes is discussed.
Polarization mode dispersion is modelled as decoherence of polarization
under the disturbance of environment and the coupling with frequency.
This model is described by the quantum master equation and the Langevin
equation. It can be predicted that the optical beam is depolarized
exponentially in a fibre and the differential group delay (DGD) is
proportional to the square root of the propagation distance. The
distribution of the DGD can also be calculated.
Calculations for a simple three‐layer slab model show that sufficient anisotropic strain birefringence can be introduced into germanosilicate, phosphosilicate, and borosilicate single‐mode fibers to reduce the coupling between orthogonally polarized modes to a level of practical interest for single‐mode single‐polarization propagation.
This paper reviews the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. It introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space. The discussion includes the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation, and the rules for PMD vector concatenation.
The authors study numerically the importance of the frequency dependence of the polarization-mode dispersion (PMD) vector to the operation of optical systems and evaluate the validity of the second-order PMD approximation. They show that there is no relevant range of parameters in which the second-order PMD approximation is useful and question the validity of considering discrete high-orders of PMD.
The Jones matrix method is used to measure the polarization mode
dispersion (PMD) of a large variety of single mode fibers in the 1500 nm
range. The dependence of PMD on wavelength, time, and temperature are
studied in two different regimes: adiabatic and isothermal. In the
adiabatic regime, time dependent stresses are introduced in the fiber by
subjecting it to large and rapid changes in temperature. In this regime
it is shown that the probability density function of PMD, obtained as a
function of temperature and wavelength, fits very closely the
theoretically predicted Maxwellian function. In the isothermal regime,
the temperature of the fiber is held constant and the stresses are
allowed to relax to their long term steady state conditions. In this
regime the PMD exhibits a strong dependence on wavelength but otherwise
is a bounded function which is nearly stationary with time. Test and
analysis of the deterministic PMD in a specially constructed
polarization maintaining fiber are used to study the dependence of PMD
on temperature and wavelength. Finally, the system implications of this
PMD study are described briefly
Recent research on fibers with very small or very large birefringence for polarization-dependent applications is reviewed. The nature of random coupling between normal modes of polarization is analyzed and discussed in connection with various applications.