The treatment of high‐dimensional problems such as the Schrödinger equation can be approached by concepts tensor product approximation. We present general techniques that used for optimization tasks and time‐dependent equations, connect them to already in many‐body quantum physics. Based on achievements from past decade, entanglement‐based methods—developed different perspectives purposes distinct communities matured provide a variety tools—can combined attack highly challenging chemistry....

The main concern of this paper is how to define proper measures multipartite entanglement for mixed quantum states. Since the structure partial separability and getting complicated if number subsystems exceeds two, one can not expect existence an ultimate scalar measure, which grasps even a small part rich hierarchical entanglement, some higher order characterizing that needed. In we make steps towards direction. First, reveal lattice-theoretic classification, introduced earlier [Sz. Szalay...

Pegasus is a graph which offers substantially increased connectivity between the qubits of quantum annealing hardware compared to Chimera. It first fundamental change in annealers built by D-Wave since Chimera was introduced 2009 and then used 2011 for D-Wave's commercial annealer. In this article we describe an algorithm defines provide what believe be best way graphically visualize order see couple each other. As supplemental material, wide variety different visualizations expose...

A recent development in quantum chemistry has established the mutual information between orbitals as a major descriptor of electronic structure. This already facilitated remarkable improvements numerical methods and may lead to more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides refined discussion theoretical concepts by introducing physical correlation its separation into classical parts distinctive quantifiers In particular,...

The operator algebra of fermionic modes is isomorphic to that qubits, the difference between them twofold: embedding subalgebras corresponding mode subsets and multiqubit subsystems on one hand, parity superselection in case other. We discuss these two fundamental differences extensively, illustrate through Jordan--Wigner representation a coherent, self-contained, pedagogical way, from point view quantum information theory. Our perspective leads us develop useful new tools for treatment...

We work out the general theory of one-parameter families partial entanglement properties and resulting depth-like quantities. Special cases these are depth partitionability, producibility (or simply depth) stretchability, which based on known earlier. also construct some further physically meaningful properties, for instance squareability, toughness, degree freedom, several ones entropic motivation. Metrological multipartite criteria with quantum Fisher information fit naturally into this...

The quantum mechanical description of the chemical bond is generally given in terms delocalized bonding orbitals, or, alternatively, correlations occupations localised orbitals. However, latter case, multiorbital were treated only two-orbital correlations, although structure far richer; and, case bonds established by more than two electrons, represent a natural point view. Here, for first time, we introduce true correlation theory, consisting framework handling toolbox measures, and...

The notions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-separability and xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-producibility are useful expressive tools for the characterization entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal partial duality between them, which is valid also their correlation counterparts. This can...

We extend the classification of mixed states quantum systems composed arbitrary numbers subsystems dimensions. This extended is complete in sense partial separability and gives $1+18+1$ classes tripartite case contrary to a former $1+8+1$. Then we give necessary sufficient criteria for these classes, which make it possible determine class state belongs. These are given by convex roof extensions functions defined on pure states. In special three-qubit systems, define different set such with...

We study the noisy GHZ-W mixture (where GHZ denotes Greenberger-Horne-Zeilinger). demonstrate some necessary but not sufficient criteria for different classes of separability these states. It turns out that partial transposition criterion Peres [Phys. Rev. Lett. 77, 1413 (1996)] and G\"uhne Seevinck [New J. Phys. 12, 053002 (2010)] dealing with matrix elements are strongest ones this two-parameter state. As a result, we determine set entangled states positive transpose.

Abstract In this work, we present a brief overview of the fermionic mode optimization within framework tensor network state methods (Krumnow et al. in Phys Rev Lett 117:210402, 2016, https://doi.org/10.1103/PhysRevLett.117.210402 ), and demonstrate that it has potential to compress multireference character wave functions after finding optimal molecular orbitals (modes), based on entanglement minimization. Numerical simulations have been performed for nitrogen dimer cc-pVDZ basis equilibrium...

Recently, the correlation theory of chemical bond was developed, which applies concepts quantum information for characterization bonds, based on multiorbital correlations within molecule. Here, first time, we extend use this mathematical toolbox description electron-deficient bonds. We start by verifying textbook example a molecule with three-center two-electron namely, diborane(6). then show that is able to properly describe bonding situation in more exotic molecules have been synthesized...

In multipartite entanglement theory, the partial separability properties have an elegant, yet complicated structure, which boils down in case when correlations are considered. this work, we elaborate this, by giving necessary and sufficient conditions for existence uniqueness of class a given class-label, use work out structure classification some important particular cases, namely, finest classification, based on k-partitionability k-producibility, atoms correlation properties.

In a recent paper it was shown that for double extremal static spherical symmetric BPS black hole solutions in the STU model well-known process of moduli stabilization at horizon can be recast form distillation procedure three-qubit entangled state Greenberger-Horne-Zeilinger type. By studying full flow space this we investigate more detail. We introduce with amplitudes depending on conserved charges, warp factor, and moduli. show recently discovered non-BPS is possible to see how unfolds...

We give explicit index-free formulae for all the degree six (and also four and two) algebraically independent local unitary invariant polynomials finite dimensional k-partite pure mixed quantum states. carry out this by use of graph-technical methods, which provides illustrations abstract topic.

Concurrence is an entanglement measure characterizing the mixed state bipartite correlations inside of a pure $n$-qubit system. We show that after organizing charges and moduli in STU model $N=2$, $d=4$ supergravity to three-qubit state, for static extremal spherically symmetric Bogomolny-Prasad-Sommerfield (BPS) black-hole solutions vanishing condition all concurrences on horizon equivalent attractor equations. As result this, macroscopic black hole entropy given by three-tangle can be...

In the past decades, quantum entanglement has been recognized to be basic resource in information theory. A fundamental need is then understanding its qualification and quantification: Is state entangled, if it is, how much carried by that? These questions introduce topics of separability criteria measures, both which are based on issue classification multipartite entanglement. this dissertation, after reviewing these three for finite dimensional Hilbert spaces, I present my contribution...

We work out the general theory of one-parameter families partial entanglement properties and resulting depth-like quantities. Special cases these are depth partitionability, producibility (or simply depth) stretchability, which based on known earlier. also construct some further physically meaningful properties, for instance squareability, toughness, degree freedom, several ones entropic motivation. Metrological multipartite criteria with quantum Fisher information fit naturally into this...

We study 12 parameter families of two qubit density matrices, arising from a special class two-fermion systems with four single particle states or alternatively four-qubit state amplitudes arranged in an antisymmetric matrix. calculate the Wooters concurrences and negativities closed form their behavior. use these results to show that relevant entanglement measures satisfy generalized Coffman-Kundu-Wootters formula distributed entanglement. An explicit for residual tangle is also given. The...