Quantitative complementarity relations in bipartite systems: Entanglement as a physical reality (original) (raw)

Complementarity and entanglement in bipartite qudit systems

Physical Review A, 2007

We consider complementarity in a bipartite quantum system of arbitrary dimensions. Single-partite and bipartite properties turn out as mutually exclusive quantities. The single-partite properties can be related to a generalized predictability and visibility which compose two complementary realities for themselves. These properties combined become mutually exclusive to the genuine quantum mechanical bipartite correlations of the system which can be quantified with the generalized I concurrence that defines a proper entanglement measure. Consequently, the complementary relation quantifies entanglement in the bipartite system. The concept of complementarity determines entanglement as a property which mutually excludes any single-partite reality. As an application, we provide a proper definition of distinguishability in an n-port interferometer.

Entanglement and Its Multipartite Extensions

International Journal of Modern Physics B, 2013

The aspects of many particle systems as far as their entanglement is concerned is highlighted. To this end we briefly review the bipartite measures of entanglement and the entanglement of pairs both for systems of distinguishable and indistinguishable particles. The analysis of these quantities in macroscopic systems shows that close to quantum phase transitions, the entanglement of many particles typically dominates that of pairs. This leads to an analysis of a method to construct many-body entanglement measures. SL-invariant measures are a generalization to quantities as the concurrence, and can be obtained with a formalism containing two (actually three) orthogonal antilinear operators. The main drawback of this antilinear framework, namely to measure these quantities in the experiment, is resolved by a formula linking the antilinear formalism to an equivalent linear framework.

Characterizing the entanglement of bipartite quantum systems

Physical Review A, 2003

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.

Entanglement monotones from complementarity relations

Journal of Physics A: Mathematical and Theoretical

Bohr’s complementarity and Schrödinger’s entanglement are two prominent physical characters of quantum systems. In this article, we formally connect them. It is known that complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate a complementarity relation and can even reach zero for a maximally mixed state. To fully characterize a quanton, it is not enough to consider its wave-particle aspect; we have also to regard its quantum correlations with other systems. Here we prove that for any complete complementarity relation involving predictability and visibility measures that satisfy the criteria established in the literature, the corresponding quantum correlations are entanglement monotones. Therefore, we formally connect entanglement monotones with complementarity relations without appealing to a particular measure.

Evaluable multipartite entanglement measures: Multipartite concurrences as entanglement monotones

Physical Review A, 2006

We discuss the monotonicity of systematically constructed quantities aiming at the quantification of the entanglement properties of multipartite quantum systems, under local operations and classical communication (LOCC). We provide a necessary and sufficient condition for the monotonicity of generalized multipartite concurrences which qualifies them as legitimate entanglement measures.

Complementary relationships between entanglement and measurement

Academia Quantum, 2024

Complementary relationships exist among interference properties of particles such as pattern visibility, predictability, and distinguishability. Additionally relationships between average information gain G ̄ and measurement disturbance F for entangled spin pairs are well established. This article examines whether a similar complementary relationship exists between entanglement and measurement. For qubit systems, both measurements on a single system and measurements on a bipartite system are considered in regard to entanglement. It is proven that E ̄ + D ≤ 1 holds, where E ̄ is the average entanglement after a measurement is made and D is a measure of the measurement disturbance of a single measurement. Assuming measurements on a bipartite system shared by Alice and Bob, it is shown that E ̄ + G ̄ ≤ 1, where G ̄ is the maximum average information gain that Bob can obtain regarding Alice’s result. These results are generalized to arbitrary initial mixed states and non-Hermitian operators. In the case of maximally entangled initial states, it is found that D ≤ EL and G ̄ ≤ EL, where EL is the loss of entanglement due to measurement by Alice. We conclude that the amount of disturbance and average information gain one can achieve is strictly limited by entanglement.

Tripartite entanglement and quantum correlation

Journal of High Energy Physics

We provide an analytical tripartite-study from the generalized R-matrix. It provides the upper bound of the maximum violation of Mermin’s inequality. For a generic 2-qubit pure state, the concurrence or R-matrix characterizes the maximum violation of Bell’s inequality. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The R-matrix gives the maximum violation of Bell’s inequality. For a general 3-qubit state, we have five invariant entanglement quantities up to local unitary transformations. We show that the five invariant quantities describe the correlation in the generalized R-matrix. The violation of Mermin’s inequality is not a proper diagnosis due to the non-monotonic behavior. We then classify 3-qubit quantum states. Each classification quantifies Quantum Entanglement by the total concurrence. In the end, we relate the experiment correlators to Quantum Entanglement.

Paradoxes of measures of quantum entanglement and Bell's inequality violation in two-qubit systems

2010

We review some counterintuitive properties of standard measures describing quantum entanglement and violation of Bell's inequality (often referred to as "nonlocality") in two-qubit systems. By comparing the nonlocality, negativity, concurrence, and relative entropy of entanglement, we show: (i) ambiguity in ordering states with the entanglement measures, (ii) ambiguity of robustness of entanglement in lossy systems and (iii) existence of two-qubit mixed states more entangled than pure states having the same negativity or nonlocality. To support our conclusions, we performed a Monte Carlo simulation of 10 6 two-qubit states and calculated all the entanglement measures for them. Our demonstration of the relativity of entanglement measures implies also how desirable is to properly use an operationally-defined entanglement measure rather than to apply formally-defined standard measures. In fact, the problem of estimating the degree of entanglement of a bipartite system cannot be analyzed separately from the measurement process that changes the system and from the intended application of the generated entanglement.