Related papers: Noiseless Quantum Circuits for the Peres Separabil…
Hilbert-Schmidt (HS) decompositions are employed for analyzing systems of n-qubits, and a qubit with a qudit. Negative eigenvalues, obtained by partial-transpose (PT) plus local unitary transformations (PTU) for one qubit from the whole…
We propose an efficient protocol to fully reconstruct a set of high-fidelity quantum gates. Usually, the efficiency of reconstructing high-fidelity quantum gates is limited by the sampling noise. Our protocol is based on a perturbative…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
It is shown that any separable state on Hilbert space ${\cal H}={\cal H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion for mixed states…
To create high-fidelity cosmic microwave background maps, current component separation methods rely on availability of information on different foreground components, usually through multi-band frequency coverage of the instrument. Internal…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
Noise in pre-fault-tolerant quantum computers can result in biased estimates of physical observables. Accurate bias-free estimates can be obtained using probabilistic error cancellation (PEC), which is an error-mitigation technique that…
We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective,…
In this study, we explore a form of quantum circuit complexity that extends to open systems. To illustrate our methodology, we focus on a basic model where the projective Hilbert space of states is depicted by the set of orientations in the…
Explicitly separable density matrices are constructed for all separable two-qubits states based on Hilbert-Schmidt (HS) decompositions. For density matrices which include only two-qubits correlations the number of HS parameters is reduced…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
In this work, we propose three-dimensional photonic circuit designs that guarantee a considerable reduction in the complexity of circuits for the purpose of performing quantum state tomography of N-dimensional path qudits. The POVM…
In this paper, we study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive…
Non-deterministic quantum noiseless linear amplifiers are a new technology with interest in both fundamental understanding and new applications. With a noiseless linear amplifier it is possible to perform tasks such as improving the…
With continuing improvements on the quality of fabricated quantum devices, it becomes increasingly crucial to analyze noisy quantum process in greater details such as characterizing the non-Markovianity in a quantitative manner. In this…
We propose a method for reconstruction of the density matrix from measurable time-dependent (probability) distributions of physical quantities. The applicability of the method based on least-squares inversion is - compared with other…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to the "local causality reversal"…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…