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

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.Comment: 10 pages, 4 figures, to appear in the Journal of Computational Methods in Sciences and Engineering -- a special issue in memory of prof. S. Kielic

EPR Paradox, Nonlocality, and Entanglement in Multi-qubit Systems

Bell inequalities were formulated by John Bell to test the possible violation of local realistic theories by quantum mechanical systems. It was shown that entangled quantu-m states of multiple particles violate various Bell’s inequalities. This proved that quan-tum mechanics allows correlations between spatially separated systems that have no classical analogue. The main focus of this work is to investigate genuine multiqubit non-locality in families of entangled 3 and 4-qubit pure states by studying a Bell-type inequality that is violated only if all qubits are non-locally correlated. We numerically study the relationship between entanglement and violation of the Svetlichny Bell-type inequality. We analyze non-local correlations in 3-qubit generalized Greenberger-Hor-ne-Zeilinger (GHZ) states, maximal slice (MS) states, and W states. Our studies show that the correlations exhibited by three particles cannot in general be described by hid-den variable theories with at most two-particle non-locality. However, some 3-qubit entangled states do not violate the Svetlichny’s inequality. We then extend our analysis to 4-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states, maximal slice (MS) states, and W states. The results are similar to the 3-qubit case for GHZ and MS states. The range of parameters for which we see a violation is the same for the 3 and 4-qubit GHZ states. However, the 4-qubit W states do not violate Bell-type inequality, unlike the 3-qubit W states. Our results show the complex nature of multiqubit entang-lement and non-locality and provide tools for designing useful quantum communica-tion tasks

Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

We formally link the concept of steering (a concept created by Schrodinger but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett. 98, 140402 (2007)] and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variables observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell-nonlocality, entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.Comment: Changed title, updated references, minor corrections, added journal-ref and DO

Quantum realism is consistent with quantum facts

Despite the unparalleled accuracy of quantum-theoretical predictions across an enormous range of phenomena, the theory's foundations are still in doubt. The theory deviates radically from classical physics, predicts counterintuitive phenomena, and seems inconsistent. The biggest stumbling block is measurement, where the Schrodinger equation's unitary evolution seems inconsistent with collapse. These doubts have inspired a variety of proposed interpretations and alterations of the theory. Most interpretations posit the theory represents only observed appearances rather than reality. The realistic interpretations, on the other hand, posit entities such as other universes, hidden variables, artificial collapse mechanisms, or human minds, that are not found in the standard mathematical formulation. Surprisingly, little attention has been paid to the possibility that the standard theory is both realistic and correct as it stands. This paper examines several controversial issues, namely quantization, field particle duality, quantum randomness, superposition, entanglement, non-locality, and measurement, to argue that standard quantum physics, realistically interpreted, is consistent with all of them.Comment: 25 pages, 5 figures, 1 tabl

Interaction-Free Effects Between Distant Atoms

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former's half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the "no exchange" result, apparently precluding entanglement, is non-locally established between the atoms by this very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell's theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of Interaction-Free-Measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework.Comment: 24 pages, 2 figures. Accepted to Foundations of Physic

Interpreting quantum nonlocality as platonic information

The "hidden variables" or "guiding equation" explanation for the measurement of quantum nonlocality (entanglement) effects can be interpreted as instantiation of Platonic information. Because these Bohm-deBroglie principles are already external to the material objects that they theoretically affect, interpreting them as Platonic is feasible. Taking an approach partially suggested by Quantum Information Theory which views quantum phenomena as sometimes observable-measurable information, this thesis defines hidden variables/guiding equation as information. This approach enables us to bridge the divide between the abstract Platonic realm and the physical world. The unobservable quantum wavefunction collapse is interpreted as Platonic instantiation. At each interaction, the wave function for a quantum system collapses. Instantly, Platonic information is instantiated in the system