Related papers: Double Dilation $\neq$ Double Mixing
We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme, the correlation…
A mixed quantum state shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of that state…
We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integral $H$, to the given system, by…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
Diagrammatic representation and manipulation of tensor networks has proven to be a useful tool in mathematics, physics, and computer science. Here we present several important and mostly well-known theorems regarding the dualities between…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
Separability of quantum states is analyzed with the use of the Choi-Jamiolkowski isomorphism. Spectral separability criteria are derived. The presented approach is illustrated with various examples, among which a separable decomposition of…
Bifractional displacement operators, are introduced by performing two fractional Fourier transforms on displacement operators. They are shown to be special cases of elements of the group G, that contains both displacements and squeezing…
For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution…
Pairwise correlation is really an important property for multi-qubit states. For the two-qubit X states extracted from Dicke states and their superposition states, we obtain a compact expression of the quantum discord by numerical check. We…
Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
We develop a technique that solders the dual aspects of some symmetry. Using this technique it is possible to combine two theories with such symmetries to yield a new effective theory. Some applications in two and three dimensional…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
A celebrated 1922 theorem of Kuratowski states that there are at most 14 distinct sets arising from applying the operations of complementation and closure, any number of times, in any order, to a subset of a topological space. In this paper…
Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…
The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the…
We investigate binary mixtures undergoing phase separation after a second (deeper) temperature quench into two- and three-phase coexistence regions. The analysis is based on a lattice theory previously developed for gas-liquid separation in…
Measurement incompatibility is one of the cornerstones of quantum theory. This phenomenon appears in many forms, of which the concept of non-joint measurability has received considerable attention in the recent years. In order to…