A new class of entanglement measures

Physical Review A, 2007

We propose an entanglement measure for two quN its based on the covariances of a set of generators of the su(N ) algebra. In particular, we represent this measure in terms of the mutually unbiased projectors for N prime. For pure states this measure quantify entanglement, we obtain an explicit expression which relates it to the concurrence hierarchy, specifically the I-concurrence and the 3concurrence. For mixed states we propose a separability criterion.

International Journal of Geometric Methods in Modern Physics, 2012

We introduce on physical grounds a new measure of multipartite entanglement for pure states. The function we define is discriminant and monotone under LOCC and moreover can be expressed in terms of observables of the system. PACS numbers:

2002

We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we concentrate on the relative entropy of entanglement with reversed entries. We show that this quantity is an entanglement monotone which is strongly additive, thereby demonstrating that monotonicity under local quantum operations and strong additivity are compatible in principle. In accordance with the presented statistical interpretation which is provided, this entanglement monotone, however, has the property that it diverges on pure states, with the consequence that it cannot distinguish the degree of entanglement of different pure states. We also prove that the relative entropy of entanglement with respect to the set of disentangled states that have identical reductions to the primary state is an entanglement monotone. We finally investigate the trace-norm measure and demonstrate that it is also a proper entanglement monotone.

Physical Review A, 2022

Concurrence introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Quantum Inf. Process. 16, 118 (2017)] for pure discrete variable systems in arbitrary dimensions and extending the concept to mixed continuous variable states. A family of faithful entanglement measures is constructed that admit necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states and non-Gaussian continuous variable Bell states, matches with known results. We also quantify entanglement of phase randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.

Arxiv preprint quant-ph/0504163, 2005

The concept of entanglement has played a crucial role in the development of quantum physics. In the early days entanglement was mainly perceived as the quali-tative feature of quantum theory that most strikingly distinguishes it from our classical intuition. The subse-quent ...

Physical Review A, 2007

We propose an entanglement measure for two qudits based on the covariances of a set of generators of the su(N) algebra. In particular, we represent this measure in terms of the mutually unbiased projectors for N prime. For pure states this measure quantify entanglement, we obtain an explicit expression which relates it to the concurrence hierarchy, specifically the I-concurrence and the 3-concurrence. For mixed states we propose a separability criterion.

arXiv (Cornell University), 2022

While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context we come up with a measure for pure states based on a geodesic distance on the space of quantum states. Our measure satisfies all the desirable properties of a "Genuine Measure of Entanglement" (GME), and in comparison with some of the other existing measures, shows better smoothness and discriminance.

We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end we derive a new decomposition for arbitrary 3-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.

Physics Letters A, 2003

In the present study we revisit the application of the q-information measures R q of Rényi's and S q of Tsallis' to the discussion of special features of two qubits systems. More specifically, we study the correlations between the qinformation measures and the entanglement of formation of a general (pure or mixed) state ρ describing a system of two qubits. The analysis uses a Monte Carlo procedure involving the 15-dimensional 2-qubits space of pure and mixed states, under the assumption that these states are uniformly distributed according to the product measure recently introduced by Zyczkowski et al [Phys. Rev. A 58 (1998) 883].

arXiv (Cornell University), 2022

While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context we come up with a measure for pure states based on a geodesic distance on the space of quantum states. Our measure satisfies all the desirable properties of a "Genuine Measure of Entanglement" (GME), and in comparison with some of the other existing measures, shows better smoothness and discriminance.