相关论文: A diagrammatic approach to map-state and channel-s…

Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…

The problem for interface solutions in the quantum theory of heterostructures comprising narrow-gap semiconductors is reformulated in the language of commutative diagrams. By this way the theory of interface states in such heterostructures…

This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…

Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes…

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…

The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…

For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected…

We propose and prove two theorems for determining the number of dark modes in linear two-component quantum networks composed of two types of bosonic modes. This is achieved by diagonalizing the two sub-networks of the same type of modes,…

A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. Using the qubit portrait method the Bell inequalities for two qubits and two qutrits are discussed in framework of…

We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…

Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…

In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…

We examine stochastic maps in the context of quantum optics. Making use of the master equation, the damping basis, and the Bloch picture we calculate a non-unital, completely positive, trace-preserving map with unequal damping eigenvalues.…

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the…

Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…

Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to one map between the product basis of quantum states comprising an arbitrary number…

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…

Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…