Calculation of quantum discord in higher dimensions for X- and other specialized states

Quantum discord, a kind of quantum correlation based on entropic measures, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. Procedures are available for analytical calculation of discord when one of the parties is a qubit with dimension two and measurements made on it to get that one-way discord. We extend now to systems when both parties are of larger dimension and of interest to qudit–quDit with d, D≥ 3 or spin chains of spins ≥ 1. While recognizing that no universal scheme is feasible, applicable to all density matrices, nevertheless, a procedure similar to that for d= 2 that works for many mixed-state density matrices remains of interest as shown by recent such applications. We focus on this method that uses unitary operations to describe measurements, reducing them to a compact form so as to minimize the number of variables needed for extremizing the classical correlation, often the most difficult part of the discord calculation. Results are boiled down to a simple recipe for that extremization; for some classes of density matrices, the procedure even gives trivially the final value of the classical correlation without that extremization. A qutrit–qutrit (d= D= 3) system is discussed in detail with specific applications to density matrices for whom other calculations involved difficult numerics. Special attention is given to the so-called X-states and Werner and isotropic states when the calculations become particularly simple. An appendix discusses an independent but related question of the systematics of X-states of arbitrary dimension. It forms a second, separate, part of this paper, extending our previous group-theoretic considerations of systematics for qubits now to higher d

What is physics? The individual and the universal, and seeing past the noise

Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in nonrelativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave, or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. It is not an element of physics. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, for an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual

Symmetries and geometries of qubits, and their uses

The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such systems for quantum information processes. In the last two decades, two different ap-proaches, with independent starting points and motivations, have been combined for this purpose. One approach has been to develop the unitary time evolution of two or more qubits in order to study quantum correlations; by exploiting the relevant Lie algebras and, especially, sub-algebras of the Hamiltonians involved, researchers have arrived at connections to finite projective geometries and combinatorial designs. Independently, geometers, by studying projective ring lines and associated finite geometries, have come to parallel conclusions. This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. Altogether, this may be seen as further development of Felix Klein’s Erlangen Program for symmetries and geometries. In particular, the fifteen generators of the continuous SU(4) Lie group for two qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite quater-nionic groups. The very different perspectives that we consider may provide further insight into quantum information problems. Extensions are considered for multiple qubits, as well as higher-spin or higher-dimensional qudits

A tale of two representations: Energy and time in photoabsorption

This essay is based on a talk at Advances in Atomic, Molecular, and Optical Sciences 2020 (AAMOS20) in a symposium honoring Prof. S. T. Manson\u27s decades-long contribution to photoabsorption studies. Quantum physics introduced into physics pairs of conjugate quantities bearing a specific complementary relationship, energy and time being one such pair. This gives rise to two alternative representations, a time-dependent and a time-independent one, seemingly very different but both capable of embracing the same physics. They give complementary descriptions and insight, with technical questions, theoretical and experimental, determining which may be the more convenient and practicable at any juncture. Two recent topics, Cooper minima in photoabsorption in Cl- and Ar, and angular-momentum barrier tunneling of f photoelectrons from Se in WSe2, provide illustrative examples, also of the role that technological developments over the past five decades played in our approach to and understanding of phenomena