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An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how magic, beyond Clifford, typical…
As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide…
We analyze the restrictions on the distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states with the time $T$…
Regions of quantum states generalize the classical notion of error bars. High posterior density (HPD) credible regions are the most powerful of region estimators. However, they are intractably hard to construct in general. This paper…
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…
Ultra-cold atoms in optical lattices provide one of the most promising platforms for analog quantum simulations of complex quantum many-body systems. Large-size systems can now routinely be reached and are already used to probe a large…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
The theory of continuous quantum measurement allows to reconstruct the state $\rho_t$ of a system from a continuous stochastic measurement record $I_t$. However, this truly continuous-time signal $I_t$ is never available in practice. In…
Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective…
A density matrix {\rho}(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t <…
We initiate an investigation into separable, but physically reasonable, states in relativistic quantum field theory. In particular we will consider the minimum amount of energy density needed to ensure the existence of separable states…
An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
A discrimination problem consists of $N$ linearly independent pure quantum states $\Phi=\{\ket{\phi_i}\}$ and the corresponding occurrence probabilities $\eta=\{\eta_i\}$. To any such problem we associate, up to a permutation over the…
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact…
We propose a method to detect genuine quantum correlation for arbitrary quantum state in terms of the rank of coefficient matrices associated with the pure state. We then derive a necessary and sufficient condition for a quantum state to…
We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states,…