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Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. Here we use methods from…
Geometric phases have been extensively investigated in a wide range of quantum systems, often revealing deep connections to the underlying topology of many-body states. In this work, we examine two geometric phases defined for mixed quantum…
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive…
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting…
Quantum computers can accurately compute ground state energies using phase estimation, but this requires a guiding state that has significant overlap with the true ground state. For large molecules and extended materials, it becomes…
We provide a definition of the quantum distances of correlated many fermion wave functions in terms of the expectation values of certain operators that we call exchange operators. We prove that the distances satisfy the triangle…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes an analogous…
Weakly nonlinear degrees of freedom in dissipative quantum systems tend to localize near manifolds of quasi-classical states. We present a family of analytical and computational methods for deriving optimal unitary model transformations…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
The quantum state overlap is the textbook measure of the difference between two quantum states. Yet, it is inadequate to compare the complex configurations of many-body systems. The problem is inherited by the widely employed quantum state…
Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales…
Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the…
Quantum state tomography, a fundamental tool for quantum physics, usually requires a number of state copies that scale exponentially with the system size, owing to the intricate quantum correlations between subsystems. We show that, in…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…
The manifold of ground states of a family of quantum Hamiltonians can be endowed with a quantum geometric tensor whose singularities signal quantum phase transitions and give a general way to define quantum phases. In this paper, we show…
We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a…