We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.
We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Third, we report the first experimental measurements of the 4 x 4 coherency matrix associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.
We report on two quantum polarization experiments. The first one shows that three geometrical rotations can in principle be distinguished with certainty using two photons. The second experiment shows quantum polarization properties of classically unpolarized light. We outline a new treatment of polarization in quantum optics. Our formalism differs from the usual quantum description, which uses the Stokes operators. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
As optical systems are one of the candidates for implementation of a scalable quantum computer, it is important to develop an adequate method of description of both quantum states of light and operations performed by optical elements. Using the concept of chi-matrix representation of quantum operations and Choi-Jamiolkowski isomorphism we expand Jones calculus to allow description of evolution of mixed polarization states in linear optical systems. The developed method is then used to give a full description of polarization echo effect, which was described in 1 based on an analogy between the effects of polarization optics and spin dynamics. Theoretical predictions are confirmed by reconstructing operations performed by a series of quartz waveplates using quantum process tomography protocols.
In the case of mixed states ρAB of the composite system A ⊗ B, the previous relation generalizes to ρAB = ∑ k pkρ A k ⊗ρk , where pk are probabilities and ρk ’s (ρk ’s) are generic density matrix of the system A (B). The entanglement derives from “subtle” nonlocal correlations between the parts of a quantum system and combines three basic structural elements of quantum theory: the superposition principle, the quantum non-separability property and the exponential scaling of the state space with the number of partitions. This unique resource can be used to perform computational and cryptographic tasks otherwise impossible with classical systems. An entangled state shared by two or more separated parties is a valuable resource for fundamental quantum protocols, such as quantum teleportation [2], quantum computing [3] and quantum cryptography. By using entangled states we can deeply investigate the nonlocal properties of the quantum world. In fact, an entangled system exhibits correlations between two (or more) parties, which cannot be reproduced by a classical theory or, in general, by a Local Hidden Variables Theory (LHVT). Quantum optics represents an excellent experimental test bench for various novel concepts introduced within the framework of quantum information theory. Quantum states of photons, generally produced by a probabilistic process, namely spontaneous parametric down conversion (SPDC), may be easily and accurately manipulated using linear and nonlinear optical devices and measured by efficient single-photon detectors. Photonic qubits represent the typical carrier of quantum information and can be distributed over long distances, either in free-space or in low-loss optical fibers. Two-particle experiments correspond to operate with qubits belonging to a (2 × 2) Hilbert space. Many quantum information tasks and fundamental tests of quantum mechanics, such as the simulation of properties of quantum systems, the realization of quantum algorithms of increasing complexity and the investigation of the quantum world at a mesoscopic level, deal with a large number of qubits. In order to take full advantage of the possibilities offered by quantum mechanics, more qubits must be added to a quantum state. Two approaches may be followed to increase the number of qubits. The first one consists of increasing the number of entangled particles. In this way, multi-qubit entangled states are created by distributing the qubits between the particles so that each particle carries one qubit. A second strategy consists of encoding more than one qubit in each particle, by exploiting different degrees of freedom (DOFs) of the photon such as the polarization, the path, the emission time, the orbital angular momentum. This has been used to create two-photon fourand six-qubit states and up to five-photon ten-qubit graph states. The entanglement of two particles in different DOFs corresponds to socalled hyperentanglement. It is worth noting that multi-qubit hyperentanglement allows to achieve higher
It takes some convincing to realize that light has a polarization degree of freedom, as our eyes are usually ignorant of light's polarization. Since overcoming this hurdle of intuition, polarization has become a fantastic resource that can be easily manipulated both physically and mathematically, opening the door to a wide variety of applications. We have only recently begun to appreciate how many more doors are opened by the quantum mechanical degrees of freedom inherent to optical polarization. One use of optical polarization is for polarimetry: measuring the changes in light's polarization after it interacts with a material is an excellent procedure for nondestructively probing the characteristics and composition of the intervening material. More sensitive measurements require brighter probe light; however, sufficiently intense light will begin to destroy the sample being probed. In this thesis, we seek to provide more sensitive polarimetry without resorting to bright beams of light. Tailoring the quantum properties of various states of light has been shown to increase their usefulness for other estimation protocols and we show how to extend this paradigm to quantum enhancements in polarimetry. We begin by finding the quantum states underlying classical polarization. Each particular set of classical polarization properties corresponds to a large variety of quantum states. Next, we establish quantum descriptions of classical polarization transformations corresponding to arbitrary Jones and Mueller matrices, including quantum mechanical insights into the distinction between processes that can and cannot be described by Jones matrices. We propose candidates for the most likely quantum states underlying classical decompositions into polarized and unpolarized fractions, carefully inspecting how these quantum states behave under polarization transformations. This language allows us to inspect quantum-enhanced sensing in the multiparameter context of polarimetry. We show the dramatic possibilities for quantum enhancements in any metrological scenario that is mathematically equivalent to a rotation, of which polarization rotations are a primary example; in contrast, we also show most attenuating and depolarizing polarization transformations to forbid such dramatic enhancements. Finally, we discuss polarization and its generalizations in the context of generating quantum entanglement via linear optics. These applications serve as mere examples of the usefulness promised by light’s quantum polarization degrees of freedom.
Abstract A general approach to the discussion of optical birefringence phenomena is presented. It is based on the S-matrix approach to photon scattering in a nonrelativistic quantum field theoretical formalism and the Stokes operator description of polarization. The use of a canonically transformed interaction Hamiltonian in combination with diagrammatic perturbation theory enables the response of a system to electromagnetic radiation to be calculated in a straightforward and consistent manner to any order in the perturbation, and the effect of static fields is included easily. As an illustration, the angle of rotation of a beam of plane-polarized light by a solution of optically active molecules is calculated and the intensity dependence of the angle determined. The latter phenomenon should become apparent at high photon flux densities particularly when ω, the frequency of the incident light, or 2ω are similar to electronic excitation frequencies in the optically active molecules.