Related papers: Extracting entanglement geometry from quantum stat…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such…
In addition to being a workhorse for modern quantum technologies, entanglement plays a key role in fundamental tests of quantum mechanics. The entanglement of photons in multiple levels, or dimensions, explores the limits of how large an…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…
We show that global properties of an unknown quantum network, such as the average degree, hub density, and the number of closed paths of fixed length, can be inferred from strictly local quantum measurements. In particular, we demonstrate…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…
In tensor-network analysis of quantum many-body systems, it is of crucial importance to employ a tensor network with a spatial structure suitable for representing the state of interest. In the previous work [Hikihara et al., Phys. Rev.…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize…
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…
We investigate a family of quantum states defined by directed graphs, where the oriented edges represent interactions between ordered qubits. As a measure of entanglement, we adopt the Entanglement Distance - a quantity derived from the…
The quantum entanglement measures for $T{\overline{T}}$ deformed field theory on boundary, deformation coefficient $\mu$, with dual bulk geometry with finite radial cutoff $\rho_c$, for entangling region is single or disjoint intervals on…
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…
Entanglement is a key resource for quantum computing, sensing, and communication, however it is highly susceptible to decoherence. To address this, quantum optics has explored filtering techniques like photon ancillas and Rydberg atom…
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure…