Related papers: Macroscopic superpositions as quantum ground state…
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
Recently, we clarify connection of spatial constraint and equilibrium macroscopic properties in disordered states of classical system under the fixed composition; namely few special microscopic states, independent of constituent elements,…
We demonstrate that a large class of first-order quantum phase transitions, namely, transitions in which the ground state energy per particle is continuous but its first order derivative has a jump discontinuity, can be described as a…
Here we present a problem related to the local Hamiltonian problem (identifying whether the ground state energy falls within one of two ranges) which is restricted to being translationally invariant. We prove that for problems with a fixed…
By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in…
Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian. First, we show the existence of a good product-state approximation for the ground-state energy of…
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…
Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside…
An operational measure to quantify the sizes of some ``macroscopic quantum superpositions'', realized in recent experiments, is proposed. The measure is based on the fact that a superposition presents greater sensitivity in interferometric…
We observe that the many-body eigenstates of any quadratic, fermionic Hamiltonian with sublattice symmetry have quantized entanglement entropies between the sublattices: the entanglement comes in multiple singlets. Moreover, such systems…
We demonstrate a break-down in the macroscopic (classical-like) dynamics of wave-packets in complex microscopic and mesoscopic collisions. This break-down manifests itself in coherent superpositions of the rotating clockwise and…