Related papers: Purification Complexity without Purifications
Quantum state purification, which operates not by identifying and correcting specific errors but by repeatedly projecting multiple noisy copies onto special subspaces, provides a syndrome-free alternative to quantum error correction.…
We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of…
The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications.…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state…
Recent work has revealed that the wave function of a pure state can be measured directly and that complementary knowledge of a quantum system can be obtained simultaneously by weak measurements. However, the original scheme applies only to…
We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two non-commuting observables only. We show that…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the…
We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the…
It is known that there are infinitely many distinguishability metrics for mixed quantum states. This freedom, in turn, leads to metric-dependent interpretations of physically meaningful geometric quantities such as complexity and volume of…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
We present a general method for constructing pure-product-state representations for density operators of $N$ quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the…
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each…
Given multiple copies of a mixed quantum state with an unknown, nondegenerate principal eigenspace, quantum state purification is the task of recovering a quantum state that is closer to the principal eigenstate. A streaming protocol…
Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the "mixed" phase, a…
An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue…