Related papers: Matrix realignment and partial transpose approach …
Inspired by the realignment or computable cross norm criterion, we present a new result about the characterization of quantum entanglement. Precisely, an interesting class of inequalities satisfied by all separable states of a bipartite…
A key problem in quantum information science is to determine optimal protocols for the interconversion of entangled states shared between remote parties. While for two parties a large number of results in this direction is available, the…
Optimal control techniques are applied for the decomposition of unitary quantum operations into a sequence of single-qubit gates and entangling operations. To this end, we modify a gradient-ascent algorithm developed for systems of coupled…
We present a generalized partial transposition separability criterion for the density matrix of a multipartite quantum system. This criterion comprises as special cases the famous Peres-Horodecki criterion and the recent realignment…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment.…
Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics…
We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle…
We present two results which combined enable one to reliably detect multimode, multipartite entanglement in the presence of measurement errors. The first result leads to a method to compute the best (approximated) physical covariance matrix…
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
Following arXiv:2210.12963 [hep-th], we investigate aspects of the time evolution operator regarded as a density operator and associated entanglement-like structures in various quantum systems. These involve timelike separations and…