首页/论文/quant-ph/0302024

arXiv quant-ph/03020242003-02quant-ph

Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation

Mark S. Byrd, Navin Khaneja

备注：: significantly rewritten and submitted for publication
发表信息：: PRA 68, 062322 (2003)
DOI：: 10.1103/PhysRevA.68.062322

英文摘要：

A parameterization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parameterization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under {\it local} unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parameterization.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

The Jamiołkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number $k$ and $k$-positive maps

Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not greater than k. It is known that such witnesses are related to k-positive maps. In this article we propose a new proof for the correspondence between vectors having Schmidt number k and k-positive maps using Jamiolkowski's criterion for positivity of linear maps; to this aim, we also investigate the precise notion of the term "Jamiolkowski isomorphism". As conse…

2007-02-27quant-ph

Generalized coherence vector applied to coherence transformations and quantifiers

One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreo…

2021-01-11quant-ph

Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality

One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer states, and there exist quantum coherence measures with respect to deterministically as well as probabilistically distinguishable sets of quantum state vectors. Here we study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors, that may not even be probabilistically distinguishable. Geometrically, a probabilistica…

2020-05-17quant-ph

Affine Maps of the Polarization Vector for Quantum Systems of Arbitrary Dimension

The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density matrix in terms of the polarization vector representation. This has been thoroughly explored for qubits since the components of the polarization vector are measurable quantities (corresponding to expectation values of Hermitian operators) and also because it enables the description of map domains geometrically. Here we extend the OS-affine map correspondence…

2010-10-12quant-ph

Master equation for non-Markovian quantum Brownian motion: The emergence of lateral coherences

Understanding the behaviour of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process of decoherence and the so-called quantum measurement problem. There have been many approaches to explore Markovian and non-Markovian dynamics within the framework of open quantum systems, but the richness of the ensuing dynamics is still not fully understood. In this paper we develop a non-Markovian extension of the standard Caldeira-Leggett model, based on…

2021-10-29quant-ph

Open system effects on slow light and electromagnetically induced transparency

The coherence properties of a three-level $Λ$-system influenced by a Markovian environment are analyzed. A coherence vector formalism is used and a vector form of the Lindblad equation is derived. Together with decay channels from the upper state, open system channels acting on the subspace of the two lower states are investigated, i.e., depolarization, dephasing, and amplitude damping channels. We derive an analytic expression for the coherence vector and the concomitant optical susceptibility, and analyze how the different channels influence the optical response. This response depends non-tr…

2011-06-20quant-ph

更多相关论文收起更多论文

Computing coherence vectors and correlation matrices, with application to quantum discord quantification

Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this article, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell Mann matrices and to compute the optimized and unoptimized versions of the associated Bloch's vectors and corre…

2016-06-30physics.comp-phquant-ph

Positivity and causal localizability in higher spin quantum field theories

It is shown that the recently introduced positivity and causality preserving string-local quantum field theory (SLFT) resolves most No-Go situations in higher spin problems. This includes in particular the Velo-Zwanziger causality problem which turns out to be related in an interesting way to the solution of zero mass Weinberg-Witten issue. In contrast to the indefinite metric and ghosts of gauge theory, SLFT uses only positivity-respecting physical degrees of freedom. The result is a fully Lorentz-covariant and causal string field theory in which light- or space-like linear strings transform …

2019-03-22hep-thmath-phmath.MP

The roles of quantum coherence in thermodynamic processes

Quantum coherence associated with the superpositions of two different sets of eigenbasis vectors has been regarded as essential in thermodynamics. It is found that coherent factors can be determined by writing observables as an expansion in the basis vectors of the systemic density operator and Hamiltonian. We reveal the roles of coherence in finite-time thermodynamic processes, such as the spin precession and the spontaneous emission of a photon. Results show that the work in the spin precession and the heat in the spontaneous emission process are mainly generated by coherence.

2022-01-28cond-mat.stat-mechquant-ph

Quantitative wave-particle duality relations from the density matrix properties

We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the corresponding closest incoherent state. Similar bounds are obtained for Wigner-Yanase's coherence. The reported inequalities are also given as coherence-populations trade-off relations. As an application example of these inequalities, we derive quantitative wave-particle duality relations for multi-slit interferometry. Our framework leads to the identificati…

2020-07-21math-phmath.MPquant-ph

将多能级量子主方程化为 Lindblad 形式以进行完全正性检验：两种方法

Bringing multilevel quantum master equations into Lindblad form for complete positivity tests: Two approaches

本文提出两种由任意 Markov 型多能级量子主方程的 Liouvillian 直接计算 Kossakowski 矩阵的方法，并用其检验 Bloch-Redfield 方程的完全正性，揭示不同三能级系统耗散动力学的相似性。

2024-11-19physics.atom-phphysics.chem-phquant-ph

相干光生过程的量子力学方面：相干性极限与多重矢量介子

Quantum mechanical aspects of coherent photoproduction: the limits of coherence, and multiple vector mesons

本文对比Good-Walker范式与半经典图像解释UPC相干光生，并指出量子干涉和超辐射可增强多重全同矢量介子产生，为观测受激衰变提供可能。

2024-04-05hep-phnucl-exnucl-th