Proposal for a quantum delayed-choice experiment

Gedanken experiments are important conceptual tools in the quest to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behaviour of the controlling devices in such experiments. We propose a framework to analyse quantum-controlled experiments and illustrate the implications by discussing a quantum version of Wheeler's delayed-choice experiment. The introduction of a quantum-controlled device (i.e., quantum beamsplitter) has several consequences. First, it implies that we can measure complementary phenomena with a single experimental setup, thus pointing to a redefinition of complementarity principle. Second, a quantum control allows us to prove there are no consistent hidden-variable theories in which "particle" and "wave" are realistic properties. Finally, it shows that a photon can have a morphing behaviour between "particle" and "wave"; this further supports the conclusion that "particle" and "wave" are not realistic properties but merely reflect how we 'look' at the photon. The framework developed here can be extended to other experiments, particularly to Bell-inequality tests

Lens Spaces and Handlebodies in 3D Quantum Gravity

We calculate partition functions for lens spaces L_{p,q} up to p=8 and for genus 1 and 2 handlebodies H_1, H_2 in the Turaev-Viro framework. These can be interpreted as transition amplitudes in 3D quantum gravity. In the case of lens spaces L_{p,q} these are vacuum-to-vacuum amplitudes \O -> \O, whereas for the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological transition amplitudes \O -> T^2 and \O -> T^2 # T^2, respectively.Comment: 14 pages, LaTeX, 5 figures, uses eps

Determinism, independence and objectivity are incompatible

Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual compatibility of apparently reasonable classical assumptions. We analyze a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (the assertion that quantum systems are, at any moment, either particles or waves, but not both). These three ideas are incompatible with any theory, not only with quantum mechanics.Comment: 4 pages, published versio

Is wave-particle objectivity compatible with determinism and locality?

Wave-particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum technologies we can test experimentally the predictions of quantum theory {\em versus} HV theories and put strong restrictions on their key assumptions. Here we study an entanglement-assisted version of the quantum delayed-choice experiment and show that the extension of HV to the controlling devices only exacerbates the contradiction. We compare HV theories that satisfy the conditions of objectivity (a property of photons being either particles or waves, but not both), determinism, and local independence of hidden variables with quantum mechanics. Any two of the above conditions are compatible with it. The conflict becomes manifest when all three conditions are imposed and persists for any non-zero value of entanglement. We propose an experiment to test our conclusions.Comment: A published version. The logic is similar to the original version, but many changes were introduce

Optimal spin-entangled electron-hole pair pump

A nonperturbative theory is presented for the creation by an oscillating potential of spin-entangled electron-hole pairs in the Fermi sea. In the weak potential limit, considered earlier by Samuelsson and Buttiker, the entanglement production is much less than one bit per cycle. We demonstrate that a strong potential oscillation can produce an average of one Bell pair per two cycles, making it an efficient source of entangled flying qubits.Comment: 6 pages including 1 figure -- Two appendices contain material that is not in the Journal version: A) Gaussian elimination for fermions; B) class of optimal pump cycle

Ground state entanglement and geometric entropy in the Kitaev model

We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and non-trivial four-body interactions between its spins. For a generic partition (A, B) of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix p(A) in the ground state. We prove that the geometric entropy associated with a region A is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state. (c) 2005 Elsevier B.V. All rights reserved

Bipartite entanglement and entropic boundary law in lattice spin systems

We investigate bipartite entanglement in spin-1/2 systems on a generic lattice. For states that are an equal superposition of elements of a group G of spin flips acting on the fully polarized state parallel to0>(xn), we find that the von Neumann entropy depends only on the boundary between the two subsystems A and B. These states are stabilized by the group G. A physical realization of such states is given by the ground state manifold of the Kitaev's model on a Riemann surface of genus g. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem A and is equal to the perimeter (up to an additive constant) when A is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i.e., no partition has zero entanglement. We also provide several examples for the square lattice

Quantum entanglement in states generated by bilocal group algebras

Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy for a bipartition (A,B) of a quantum system and conditions to saturate it. We show that these states can be interpreted as ground states of generic Hamiltonians or as the physical states in a quantum gauge theory and that under specific conditions their geometric entropy satisfies the entropic area law. If G is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (i.e., bipartite) graph states and they include Greenberger-Horne-Zeilinger, cluster states, etc. Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states

Quantum control in foundational experiments

We describe a new class of experiments designed to probe the foundations of quantum mechanics. Using quantum controlling devices, we show how to attain a freedom in temporal ordering of the control and detection of various phenomena. We consider wave-particle duality in the context of quantum-controlled and the entanglement-assisted delayed-choice experiments. Then we discuss a quantum-controlled CHSH experiment and measurement of photon's transversal position and momentum in a single set-up.Comment: Contribution to the Proceedings of the workshop Horizons of Quantum Physics, Taipei, 14-18.10.2012. Published version: two new authors, modified and streamlined presentation, new section on quantum control in complementary position/momentum measurement