相关论文: Local Unitary Invariants of Quantum States
We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…
We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We…
In previous work the authors introduced a notion of generic states and obtained criteria for local equivalence of them. Here they introduce the concept of CHG states maintaining the criteria of local equivalence. This fact allows the…
In the present paper few steps are undertaken towards the description of the qubit-qutrit pair - quantum bipartite system composed of two and three level subsystems. The computational difficulties with the construction of the local unitary…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
In this paper we present a modified version of the proof given Jing-Yang-Zhao's paper "Local Unitary Equivalence of Quantum States and Simultaneous Orthogonal Equivalence," which established the correspondence between local unitary (LU)…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the…
We present two general methods to implement quantum circuits for the direct measuring of local unitary invariants on quantum computers. We work these out for important three-qubit invariants, and also demonstrate these on the IBM Quantum…
We study the localization properties of bipartite channels, whose action on a subsystem yields a unitary channel. In particular we show that, under such channel, the subsystem must evolve independent of its environment. This point of view…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure…
An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…
We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine…
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if…
We present that the local unitary equivalence of n-party pure states is consistent with the one of their (n-1)-party reduced density matrices. As an application, we obtain the local invariants for a class of tripartite pure qudits.
In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…