scholarly journals Rays, waves, SU(2) symmetry and geometry: toolkits for structured light

2021 ◽  
Author(s):  
Yijie Shen
Keyword(s):  
Degrees Of Freedom ◽  
Structured Light ◽  
High Capacity ◽  
Quantum States ◽  
Geometric Transformation ◽  
Quantum Communications ◽  
Dimensional Control ◽  
General Symmetry ◽  
Higher Dimensional ◽  
Mathematics And Physics

Abstract Structured light refers to the ability to tailor optical patterns in all its degrees of freedom, from conventional 2D transverse patterns to exotic forms of 3D,4D, and even higher-dimensional modes of light, which break fundamental paradigms and open new and exciting applications for both classical and quantum scenarios. The description of diverse degrees of freedom of light can be based on different interpretations, e.g. rays, waves, and quantum states, that are based on different assumptions and approximations. In particular, recent advances highlighted the exploiting of geometric transformation under general symmetry to reveal the "hidden" degrees of freedom of light, allowing access to higher dimensional control of light. In this tutorial, I outline the basics of symmetry and geometry to describe light, starting from the basic mathematics and physics of SU(2) symmetry group, and then to the generation of complex states of light, leading to a deeper understanding of structured light with connections between rays and waves, quantum and classical. The recent explosion of related applications are reviewed, including advances in multi-particle optical tweezing, novel forms of topological photonics, high-capacity classical and quantum communications, and many others, that, finally, outline what the future might hold for this rapidly evolving field.

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

QUANTIZATION OF REDUCED CHERN–SIMONS GRAVITY WITH A SOURCE

2004 ◽  
Vol 19 (28) ◽  
pp. 4883-4897 ◽  
Author(s):  
A. V. NAZARENKO
Keyword(s):  
Continuous Spectrum ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Quantum States ◽  
Theory Of Constraints ◽  
Volume Operator ◽  
Modular Transformations ◽  
Probability Of Transition ◽  
Chern Simons

Using the Dirac's theory of constraints, procedure of reduction of field degrees of freedom, whose number is restricted by equations of motion and topological conditions, is proposed. Such a procedure is applied in the case of space with the topology of a torus to the Chern–Simons gravity generalized by inclusion of a source. It is shown that in this system some modular transformations preserving the volume do not lead to physically equivalent states. Such a breaking of modular symmetry reduces the degeneration of quantum states with preservation of continuous spectrum of the volume operator. Probability of transition between spaces of different volumes is computed.

scholarly journals Husimi–Wigner representation of chaotic eigenstates

2008 ◽  
Vol 464 (2094) ◽  
pp. 1503-1524 ◽  
Author(s):  
Fabricio Toscano ◽  
Anatole Kenfack ◽  
Andre R.R Carvalho ◽  
Jan M Rost ◽  
Alfredo M Ozorio de Almeida
Keyword(s):  
Hilbert Space ◽  
Coherent State ◽  
Pure State ◽  
Degrees Of Freedom ◽  
Factor Space ◽  
Wigner Functions ◽  
Higher Dimensional ◽  
Wigner Representation ◽  
Quantum Point ◽  
The Individual

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of non-classical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual two-dimensional Wigner functions resemble those of semiclassically quantized states.

Quantum readout of Physical Unclonable Functions

2012 ◽  
Vol 10 (01) ◽  
pp. 1250001 ◽  
Author(s):  
BORIS ŠKORIĆ
Keyword(s):  
Quantum State ◽  
Degrees Of Freedom ◽  
Quantum Computer ◽  
Single Photon ◽  
Trusted Computing ◽  
A Priori ◽  
Special Property ◽  
Quantum States ◽  
Unique Challenge ◽  
Physical Unclonable Functions

Physical unclonable functions (PUFs) are physical structures that are hard to clone and have a unique challenge-response behavior. The term PUF was coined by Pappu et al. in 2001. That work triggered a lot of interest, and since then a substantial number of papers has been written about the use of a wide variety of physical structures for different security purposes such as identification, authentication, read-proof key storage, key distribution, tamper evidence, anti-counterfeiting, software-to-hardware binding and trusted computing. In this paper we propose a new security primitive: the quantum-readout PUF (QR-PUF). This is a classical PUF, without internal quantum degrees of freedom, which is challenged using a quantum state, e.g. a single-photon state, and whose response is also a quantum state. By the no-cloning property of unknown quantum states, attackers cannot intercept challenges or responses without noticeably disturbing the readout process. Thus, a verifier who sends quantum states as challenges and receives the correct quantum states back can be certain that he is probing a specific QR-PUF without disturbances, even if the QR-PUF is far away "in the field" and under hostile control. For PUFs whose information content is not exceedingly large, all currently known PUF-based authentication and anti-counterfeiting schemes require trusted readout devices in the field. Our quantum readout scheme has no such requirement. Furthermore, we show how the QR-PUF authentication scheme can be interwoven with quantum key exchange (QKE), leading to an authenticated QKE protocol between two parties. This protocol has the special property that it requires no a priori secret shared by the two parties, and that the quantum channel is the authenticated channel, allowing for an unauthenticated classical channel. We provide security proofs for a limited class of attacks. The proofs depend on the physical unclonability of PUFs and on the practical infeasibility of building a quantum computer.

Security analysis of KXB10 QKD protocol with higher-dimensional quantum states

2021 ◽  
pp. 2150005
Author(s):  
Usama Ahsan ◽  
Muhammad Mubashir Khan ◽  
Asad Arfeen ◽  
Khadija Azam
Keyword(s):  
Quantum Key Distribution ◽  
Security Analysis ◽  
Higher Dimensions ◽  
Transmission Error ◽  
Quantum States ◽  
Higher Dimensional ◽  
Implementation Techniques ◽  
Generalized Dimension ◽  
Secret Keys ◽  
Qubit States

Quantum key distribution (QKD) is one of the exciting applications of quantum mechanics. It allows the sharing of secret keys between two communicating parties with unconditional security. A variety of QKD protocols have been proposed since the inception of the BB84 protocol. Among different implementation techniques of QKD protocols, there is a category which exploits higher dimensions qubit states to encode classical bits. In this paper, we focus on such a QKD protocol called KXB10, which uses three bases with higher dimensions. Analysis of the generalized dimension quantum states is performed by evaluating it based on the index transmission error rate ITER. We find that there is a direct relationship between qubit dimensions and ITER for the KXB10 protocol.

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