EISSN : 1314-7374
Published by: Quanta (10.12743)
Total articles ≅ 66
Latest articles in this journal
Quanta, Volume 11, pp 5-14; https://doi.org/10.12743/quanta.v11i1.189
We review how the kinematic structures of special relativity and quantum mechanics both stem from the relativity principle, i.e., "no preferred reference frame" (NPRF). Essentially, NPRF applied to the measurement of the speed of light c gives the light postulate and leads to the geometry of Minkowski space, while NPRF applied to the measurement of Planck's constant h gives "average-only" projection and leads to the denumerable-dimensional Hilbert space of quantum mechanics. These kinematic structures contain the counterintuitive aspects ("mysteries") of time dilation, length contraction, and quantum entanglement. In this essay, we extend the application of NPRF to the gravitational constant G and show that it leads to the "mystery" of the contextuality of mass in general relativity. Thus, we see an underlying coherence and integrity in modern physics via its "mysteries" and the fundamental constants c, h, and G. It is well known that Minkowski and Einstein were greatly influenced by David Hilbert in their development of special relativity and general relativity, respectively, but relating those theories to quantum mechanics via its non-Boolean Hilbert space kinematics is perhaps surprising.Quanta 2022; 11: 5–14.
Quanta, Volume 11, pp 15-27; https://doi.org/10.12743/quanta.v11i1.197
We first show that every operation possesses an unique dual operation and measures an unique effect. If a and b are effects and J is an operation that measures a, we define the sequential product of a then b relative to J. Properties of the sequential product are derived and are illustrated in terms of Lüders and Holevo operations. We next extend this work to the theory of instruments and observables. We also define the concept of an instrument (observable) conditioned by another instrument (observable). Identity, state-constant and repeatable instruments are considered. Sequential products of finite observables relative to Lüders and Holevo instruments are studied.
Quanta, Volume 11, pp 1-4; https://doi.org/10.12743/quanta.v11i1.180
I revisit Jordan's derivation of Einstein's formula for energy fluctuations in the black body in thermal equilibrium. This formula is usually taken to represent the unification of the wave and the particle aspects of the electromagnetic field since the fluctuations can be shown to be the sum of wave-like and particle-like contributions. However, in Jordan's treatment there is no mention of the Planck distribution and all averages are performed with respect to pure number states of radiation (mixed states had not yet been discovered!). The chief reason why Jordan does reproduce Einstein's result despite not using thermal states of radiation is that he focuses on fluctuations in a small (compared to the whole) volume of the black body. The state of radiation in a small volume is highly entangled to the rest of the black body which leads to the correct fluctuations even though the overall state might, in fact, be assumed to be pure (i.e. at zero temperature). I present a simple derivation of the fluctuations formula as an instance of mixed states being reductions of higher level pure states, a representation that is affectionately known as "Church of the Higher Hilbert Space". According to this view of mixed states, temperature is nothing but the amount of entanglement between the system and its environment.Quanta 2022; 11: 1–4.
Quanta, Volume 10, pp 34-41; https://doi.org/10.12743/quanta.v10i1.165
In their seminal 1961 paper, Sudarshan, Mathews and Rau investigated properties of the dynamical A and B maps acting on n-dimensional quantum systems. The nature of dynamical maps in open quantum system evolutions has attracted great deal of attention in the later years. However, the novel paper on the A and B dynamical maps has not received its due attention. In this tutorial article, we review the properties of A and B forms associated with the dynamics of finite dimensional quantum systems. In particular, we investigate a canonical structure associated with the A form and establish its equivalence with the associated B form. We show that the canonical structure of the A form captures the completely positive (not completely positive) nature of the dynamics in a succinct manner. This feature is illustrated through physical examples of qubit channels.Quanta 2021; 10: 34–41.
Quanta, Volume 10, pp 65-74; https://doi.org/10.12743/quanta.v10i1.173
A satisfactory resolution of the persistent quantum measurement problem remains stubbornly unresolved in spite of an overabundance of efforts of many prominent scientists over the decades. Among others, one key element is considered yet to be resolved. It comprises of where the probabilities of the measurement outcome stem from. This article attempts to provide a plausible answer to this enigma, thus eventually making progress toward a cogent solution of the longstanding measurement problem.Quanta 2021; 10: 65–74.
Quanta, Volume 10; https://doi.org/10.12743/quanta.v10i1.148
We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a geometrical interpretation of quantum mechanics.Quanta 2021; 10: 1–14.
Quanta, Volume 10, pp 55-64; https://doi.org/10.12743/quanta.v10i1.162
In this work, we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type canonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touched upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin.Quanta 2021; 10: 55–64.
Quanta, Volume 10, pp 75-104; https://doi.org/10.12743/quanta.v10i1.174
George Sudarshan has been hailed as a titan in physics and as one who has made some of the most significant contributions in several areas of physics. This article is an attempt to highlight the seminal contributions he has made in physics and the significant developments that arose from his work.Quanta 2021; 10: 75–104.
Quanta, Volume 10, pp 22-33; https://doi.org/10.12743/quanta.v10i1.159
A procedure allowing to construct rigorously discrete as well as continuum deterministic evolution equations from stochastic evolution equations is developed using Dirac's bra–ket notation. This procedure is an extension of an approach previously used by the author coined Discrete Stochastic Evolution Equations. Definitions and examples of discrete as well as continuum one-dimensional lattices are developed in detail in order to show the basic tools that allow to construct Schrödinger-like equations. Extension to multi-dimensional lattices are studied in order to provide a wider exposition and the one-dimensional cases are derived as special cases, as expected. Some variants of the procedure allow the construction of other evolution equations. Also, using a limiting procedure, it is possible to derive the Schrödinger equation from the Schrödinger-like equations. Another possible approach is given in the appendix.Quanta 2021; 10: 22–33.
Quanta, Volume 10, pp 15-21; https://doi.org/10.12743/quanta.v10i1.163
Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much less studied. Here we overview how the quantum Sinkhorn theorem can be successfully applied to find a two-qubit entangled state which has the strongest robustness against local noises and losses of quantum information carriers. We solve a practically relevant problem of finding an optimal initial encoding to distribute entangled polarized qubits through communication lines with polarization dependent losses and extra depolarizing noise. The longest entanglement lifetime is shown to be attainable with a state that is not maximally entangled.Quanta 2021; 10: 15–21.