相关论文: Highly entangled tensors

Quantum entanglement is a unique correlation phenomenon in quantum mechanics, and the measurement of quantum entanglement plays an important role in quantum computing and quantum communication. Many mainstream entanglement criteria and…

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue.…

Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…

Entanglement of formation quantifies the entanglement of a state in terms of the entropy of entanglement of the least entangled pure state needed to prepare it. An analytical expression for this measure exists only for special cases, and…

We prove that the general tensor of size 2^n and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.9997 (2^n)/(n+1) (the constant 1 being the optimal value). Similarly, the general tensor of size 3^n and rank k…

We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators.This expression is especially useful for…

We generalize previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the Quantum Relative Entropy and Bures Metric generate two…

For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled…

We present a class of entanglement identifiers which has the following experimentally friendly feature: once the expectation value of the identifier exceeds some definite limit, we can conclude the state is entangled, even if not all…

We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on entanglement measures, we prove a sharpened…

High-dimensional encoding of quantum information provides a promising method of transcending current limitations in quantum communication. One of the central challenges in the pursuit of such an approach is the certification of…

The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…

In this paper, we consider higher order paired symmetric tensors and strongly paired symmetric tensors. Elasticity tensors and higher order elasticity tensors in solid mechanics are strongly paired symmetric tensors. A (strongly) paired…

We introduce geometric measures of entanglement for indistinguishable particles, which apply to mixed states, multipartite systems, and arbitrary dimensions. They are based on generalized (i.e., not necessarily finite) norms on the set of…

Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \epsilon} the measure of those t \in [T;2T] for which log |\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard…

We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…

A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

In this paper, we investigate a genuine multipartite entanglement measure based on the geometric method. This measure arrives at the maximal value for the absolutely maximally entangled states and has desirable properties for quantifying…

We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are…