Class Of Mixed States Research Articles

Logarithmic negativity in quantum Lifshitz theories

We investigate quantum entanglement in a non-relativistic critical system by calculating the logarithmic negativity of a class of mixed states in the quantum Lifshitz model in one and two spatial dimensions. In 1+1 dimensions we employ a correlator approach to obtain analytic results for both open and periodic biharmonic chains. In 2+1 dimensions we use a replica method and consider spherical and toroidal spatial manifolds. In all cases, the universal finite part of the logarithmic negativity vanishes for mixed states defined on two disjoint components. For mixed states defined on adjacent components, we find a non-trivial logarithmic negativity reminiscent of two-dimensional conformal field theories. As a byproduct of our calculations, we obtain exact results for the odd entanglement entropy in 2+1 dimensions.

Measure of quantum correlations that lies approximately between entanglement and discord

When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally by a wider class of measures such as the quantum discord. In this work, I introduce a simple thought experiment defining a new measure of quantum correlations, which I call the accord, and write the result as a minimax optimization over unitary matrices. I find the exact result for pure states as a simple function of the Schmidt coefficients and provide a complete proof, and I likewise provide and prove the result for several classes of mixed states, notably including all states of two qubits and the experimentally relevant case of a pure state mixed with colorless noise. I demonstrate that for two qubit states the accord provides a tight lower bound on the discord; for Bell diagonal states it is also an upper bound on entanglement.

Estimation of entanglement negativity of a two-qubit quantum system with two measurements

Numerous work had been done to quantify the entanglement of a two-qubit quantum state, but it can be seen that previous works were based on joint measurements on two copies or more than two copies of the quantum state under consideration. In this work, we show that a single copy and two measurements are enough to estimate the entanglement quantifier like entanglement negativity and concurrence. To achieve our goal, we establish a relationship between the entanglement negativity and the minimum eigenvalue of the structural physical approximation of the partial transpose of an arbitrary two-qubit state. The derived relation makes it possible to estimate entanglement negativity experimentally by Hong-Ou-Mandel interferometry with only two detectors. Also, we derive the upper bound of the concurrence of an arbitrary two-qubit state and have shown that the upper bound can be realized in experiment. We will further show that the concurrence of i) an arbitrary pure two-qubit state and ii) a particular class of mixed states, namely, rank-2 quasi-distillable mixed states, can be exactly estimated with two measurements.

Non-monotonicity of Trace Distance Under Tensor Products

The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not shows up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states.

Heuristic for estimation of multiqubit genuine multipartite entanglement

For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature.

General depolarized pure states: Identification and properties

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some multipartite pure states. Here a generalized Schmidt decomposition is given for states which are equivalent to depolarized pure states. Experimental methods for the identification of this class of mixed states are provided and some examples are discussed which show the utility of this description. A particularly interesting example provides, for the first time, an interpretation of the number of negative eigenvalues of the density matrix.

Entanglement change of mixed states under canonical unitary operations in two qubits

We investigate entanglement change of mixed states in a class by applying canonical unitary form of two-qubit unitary operations. The class, including Werner states, Bell diagonal states and maximum entangled mixed states, is characterized by three real parameters and geometrically presented by a tetrahedron. We propose a class of mixed states whose entanglement cannot be increased by any canonical unitary operation.

Square-root measurement for quantum symmetric mixed state signals

A certain class of mixed states artificially constructed that is used in quantum cryptography is crucial for representation of signals. This correspondence shows that the square-root measurement gives the optimal measurement for such a class of mixed states.

The Relative Entropy of Entanglement of Schmidt Correlated States and Distillation

We show that a mixed state ρ = ∑mnamn|m〉〈n| can be realized by an ensemble of pure states {pk, |pk〉} where |\phi_k\rangle\ = \sum_m \sqrt{a_mm} e^{i\theta^k_m}|m\rangle. Employing this form, we discuss the relative entropy of entanglement of Schmidt correlated states. Also, we calculate the distillable entanglement of a class of mixed states. PACS: 03.67.-a; 03.65.Bz; 03.65.Ud

Observations of quantum dynamics by solution‐state NMR spectroscopy

NMR is emerging as a valuable testbed for the investigation of foundational questions in quantum mechanics. The present article outlines the preparation of a class of mixed states, called pseudo-pure states, that emulate pure quantum states in highly mixed solution-state NMR samples. It also describes the NMR observation of spinor behavior in spin ½ nuclei, the simulation of wave function collapse using a magnetic field gradient, the creation of entangled (i.e., Bell) pseudo-pure states, and a brief discussion of quantum computing logic gates including the Quantum Fourier Transform. These experiments show that solution-state NMR can be used to demonstrate quantum dynamics at a level suitable for laboratory exercises. ©1999 John Wiley & Sons, Inc. Concepts Magn Reson 11: 225–238, 1999