Related papers: Purifications of multipartite states: limitations …
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI)…
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In…
We study six natural decompositions of mixed states in one spatial dimension: the Matrix Product Density Operator (MPDO) form, the local purification form, the separable decomposition (for separable states), and their three translational…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
Purification of mixed states in Quantum Mechanics, by which we mean the transformation into pure states, has been viewed as an {\it Operation} in the sense of Kraus et al and explicit {\it Kraus Operators} \cite{kra1,kra2,kra3} have been…
We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states, and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in different partners of…
Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system S have been developed in the past years. In this letter we present a new approach, based…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
The operator Schmidt rank is the minimum number of terms required to express a state as a sum of elementary tensor factors. Here we provide a new proof of the fact that any bipartite mixed state with operator Schmidt rank two is separable,…
Purification is a tool that allows to represent mixed quantum states as pure states on enlarged Hilbert spaces. A purification of a given state is not unique and its entanglement strongly depends on the particular choice made. Moreover, in…
In this paper we consider feedback control algorithms for the rapid purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show 1) that the algorithm that maximizes the average…
We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix…
We develop two cutting-edge approaches to construct deep neural networks representing the purified finite-temperature states of quantum many-body systems. Both methods commonly aim to represent the Gibbs state by a highly expressive…
We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii)…
A method for producing an upper bound for all multipartite purification protocols is devised, based on knowing the optimal protocol for purifying bipartite states. When applied to a range of noise models, both local and correlated, the…
We introduce a new decomposition of the multiqubit states of the form $\rho^{\otimes N}$ and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state…
We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have…