Related papers: A geometric Fano--Procrustes framework for purific…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
Purification is a process in which decoherence is partially reversed by using several input systems which have been subject to the same noise. The purity of the outputs generally increases with the number of input systems, and decreases…
Error filtration is a hardware scheme that mitigates noise by exploiting auxiliary qubits and entangling gates. Although both signal and ancillas are subject to local noise, constructive interference(and in some cases post-selection) allows…
In Ref. [1], we proved a duality between two optimizations problems. The primary one is, given two quantum channels M and N, to find a quantum channel R such that RN is optimally close to M as measured by the worst-case entanglement…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
It is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by $2\times 2$ density matrices is just the path ordered product of Thomas rotations. These rotations are invariant under hyperbolic…
Quantum networks rely on high-fidelity entanglement links, but achieving target fidelity often increases latency and Bell pair consumption due to purification. This paper proposes a cost-based scheduler that jointly optimizes path selection…
Topology optimization of a waveguide-cavity structure in phononic crystals for designing narrow band filters under the given operating frequencies is presented in this paper. We show that it is possible to obtain an ultra-high-Q filter by…
We reveal the noncyclic Pancharatnam phase--arising from the coherent system-meter interaction--as a fundamental criterion that governs the optimal performance of quantum compression channels in postselected metrology. This phase embodies a…
Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to…
The quantum steering ellipsoid inscribed inside the Bloch sphere offers an elegant geometric visualization of two-qubit states shared between Alice and Bob. The set of Bloch vectors of Bob's qubit, steered by Alice via all possible local…
Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information respect to the tomography result. Convex…
We enhance our quantitative comprehension of the complexity associated with both time-optimal and time sub-optimal quantum Hamiltonian evolutions that connect arbitrary source and target states on the Bloch sphere, as recently presented in…
Entanglement is a key resource for quantum computing, sensing, and communication, however it is highly susceptible to decoherence. To address this, quantum optics has explored filtering techniques like photon ancillas and Rydberg atom…
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dynamics, however, the reduced evolution is described by quantum…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
In [J. C. Howell and J. A. Yeazell, Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. We model the decoherence due to light…
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…
The constrained orthogonal Procrustes problem is the least-squares problem that calls for a rotation matrix that optimally aligns two matrices of the same order. Over past decades, the algorithm of choice for solving this problem has been…
The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by…