相关论文: A mathematical proof for a ground-state identifica…

In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…

Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in the state space, and that a certificate requires a tomographic reconstruction…

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…

We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…

We first propose a new separability criterion based on algebraic-geometric invariants of bipartite mixed states introduced in [1], then prove that for all low ranks r <m+n-2, generic rank r mixed states in mxn systems have relatively high…

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

This short note describes a method to tackle the (bipartite) quantum separability problem. The method can be used for solving the separability problem in an experimental setting as well as in the purely mathematical setting. The idea is to…

We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and…

Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on…

We prove that any three linearly independent pure quantum states can always be locally distinguished with nonzero probability regardless of their dimension, entanglement, or multipartite structure. Almost always, all three states can be…

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial…

The reduction criterion is a well known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a new set of necessary conditions for separability of…

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…

Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…

Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…

Let K be an algebraic function field of characteristic 2 with constant field C_K. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u,x of K with u…

Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…

Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and…

We derive a combinatorial criterion for detecting k-separability of N-partite Dicke states. The criterion is efficiently computable and implementable without full state tomography. We give examples in which the criterion succeeds, where…

The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to…