scholarly journals Generalized Spin Bases for Quantum Chemistry and Quantum Information

2008 ◽  
Vol 73 (10) ◽  
pp. 1281-1298 ◽  
Author(s):  
Maurice R. Kibler
Keyword(s):  
Quantum Information ◽  
Quantum Chemistry ◽  
Prime Number ◽  
Complete Solution ◽  
Quantum Systems ◽  
Cyclic Symmetry ◽  
Information Share ◽  
Pauli Matrices ◽  
Starting Point ◽  
Hilbert Subspace

Symmetry-adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information and quantum computation. Our approach is based on the use of generalized Pauli matrices arising from a polar decomposition of SU(2). This approach leads to a complete solution for the construction of mutually unbiased bases in the case where the dimension d of the considered Hilbert subspace is a prime number. We also give the starting point for studying the case where d is the power of a prime number. A connection of this work to the unitary group U(d) and the Pauli group is briefly underlined.

Thermodynamics and Control of Open Quantum Systems

2021 ◽  
Author(s):  
Gershon Kurizki ◽  
Abraham G. Kofman
Keyword(s):  
Quantum Chemistry ◽  
Quantum Physics ◽  
Open Quantum Systems ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Open Quantum ◽  
Heat Engines ◽  
Chemistry Research ◽  
And Control ◽  
Quantum Thermodynamic

The control of open quantum systems and their associated quantum thermodynamic properties is a topic of growing importance in modern quantum physics and quantum chemistry research. This unique and self-contained book presents a unifying perspective of such open quantum systems, first describing the fundamental theory behind these formidably complex systems, before introducing the models and techniques that are employed to control their quantum thermodynamics processes. A detailed discussion of real quantum devices is also covered, including quantum heat engines and quantum refrigerators. The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.

scholarly journals Topological protection of biphoton states

Science ◽  
2018 ◽  
Vol 362 (6414) ◽  
pp. 568-571 ◽  
Author(s):  
Andrea Blanco-Redondo ◽  
Bryn Bell ◽  
Dikla Oren ◽  
Benjamin J. Eggleton ◽  
Mordechai Segev
Keyword(s):  
Quantum Information ◽  
Thermal Environment ◽  
Propagation Constant ◽  
Quantum Systems ◽  
Quantum Gates ◽  
Scattering Loss ◽  
Spatial Features ◽  
Quantum Optical ◽  
Nontrivial Topology ◽  
Large Quantum

The robust generation and propagation of multiphoton quantum states are crucial for applications in quantum information, computing, and communications. Although photons are intrinsically well isolated from the thermal environment, scaling to large quantum optical devices is still limited by scattering loss and other errors arising from random fabrication imperfections. The recent discoveries regarding topological phases have introduced avenues to construct quantum systems that are protected against scattering and imperfections. We experimentally demonstrate topological protection of biphoton states, the building block for quantum information systems. We provide clear evidence of the robustness of the spatial features and the propagation constant of biphoton states generated within a nanophotonics lattice with nontrivial topology and propose a concrete path to build robust entangled states for quantum gates.

ENCRYPTION OF QUANTUM INFORMATION

2003 ◽  
Vol 14 (05) ◽  
pp. 741-755 ◽  
Author(s):  
JAN BOUDA ◽  
VLADIMÍ R. BUŽEK
Keyword(s):  
Quantum Information ◽  
Quantum Channel ◽  
Composite System ◽  
Quantum Systems ◽  
Noisy Channel ◽  
Classical Description ◽  
Quantum Analogue ◽  
Known Plaintext Attack

We study in detail the problem of encryption of quantum information. We present an attack on a private quantum channel (PQC) which applies when partial classical description of a ciphertext is known (the so-called known-ciphertext attack) and we show how this situation can be avoided. The quantum analogue of the known plaintext attack is also discussed. We determine how correlations between quantum systems can be encrypted and we conclude that two PQCs on the subsystems form a PQC on the whole composite system. Finally, some applications of the PQC are suggested and a security of a noisy channel is discussed.

scholarly journals Quantum state space dimension as a quantum resource

2015 ◽  
Vol 13 (06) ◽  
pp. 1550039 ◽  
Author(s):  
A. Plastino ◽  
G. Bellomo ◽  
A. R. Plastino
Keyword(s):  
Quantum Information ◽  
State Space ◽  
Quantum State ◽  
Space Dimension ◽  
Quantum Systems ◽  
Quantum States ◽  
Information Tasks

We argue that the dimensionality of the space of quantum systems’ states should be considered as a legitimate resource for quantum information tasks. The assertion is supported by the fact that quantum states with discord-like capacities can be obtained from classically-correlated states in spaces of dimension large enough. We illustrate things with some simple examples that justify our claim.

scholarly journals Quantum technologies with hybrid systems

2015 ◽  
Vol 112 (13) ◽  
pp. 3866-3873 ◽  
Author(s):  
Gershon Kurizki ◽  
Patrice Bertet ◽  
Yuimaru Kubo ◽  
Klaus Mølmer ◽  
David Petrosyan ◽  
...  
Keyword(s):  
Quantum Information ◽  
Secure Communication ◽  
Quantum Information Processing ◽  
Quantum Systems ◽  
Quantum States ◽  
Current Direction ◽  
Ongoing Effort ◽  
Hybrid Quantum Systems ◽  
Physical Components

An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.

scholarly journals On Finite Groups With ‘Hidden’ Primes

1971 ◽  
Vol 12 (3) ◽  
pp. 287-300 ◽  
Author(s):  
L. G. Kovács ◽  
Joachim Neubüser ◽  
B. H. Neumann
Keyword(s):  
Finite Group ◽  
Prime Number ◽  
Cyclic Group ◽  
Finite Groups ◽  
Infinite Order ◽  
Proper Subset ◽  
Minimal Set ◽  
Minimal Sets ◽  
Starting Point

The starting point of this investigation was a question put to us by Martin B. Powell: If the prime number p divides the order of the finite group G, must there be a minimal set of generators of G that contains an element whose order is divisible by p? A set of generators of G is minimal if no set with fewer elements generates G. A minimal set of generators is clearly irredundant, in the sense that no proper subset of it generates G; an irredundant set of generators, however, need not be minimal, as is easily seen from the example of a cyclic group of composite (or infinite) order. Powell's question can be asked for irredundant instead of minimal sets of generators; it turns out that the answer is not the same in these two cases. A different formulation, together with some notation, may make the situation clearer.

scholarly journals Experimental quantification of spatial correlations in quantum dynamics

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 90 ◽  
Author(s):  
Lukas Postler ◽  
Ángel Rivas ◽  
Philipp Schindler ◽  
Alexander Erhard ◽  
Roman Stricker ◽  
...  
Keyword(s):  
Quantum Information ◽  
Quantum Dynamics ◽  
Quantum Information Processing ◽  
Tomographic Reconstruction ◽  
Quantum Systems ◽  
Theoretical Research ◽  
Spatial Correlations ◽  
Correlation Measure ◽  
Quantum Process ◽  
Composite Quantum System

Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [Á. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for two- and four-qubit systems. The method proposed and demonstrated in this work is scalable, platform-independent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures.

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