Multisetting Bell-type inequalities for detecting genuine tripartite entanglement

In a recent paper, Bancal et al. put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a lab without resorting to any knowledge of the dimension of the state space or of the specific form of the measurement operators. As a by-product they found a three-party three-setting Bell inequality which enables to detect genuine tripartite entanglement in a noisy 3-qubit Greenberger-Horne-Zeilinger (GHZ) state for visibilities as low as 2/3 in a device-independent way. In this paper, we generalize this inequality to an arbitrary number of settings, demonstrating a threshold visibility of 2/pi~0.6366 for number of settings going to infinity. We also present a pseudo-telepathy Bell inequality achieving the same threshold value. We argue that our device-independent witnesses are optimal in the sense that the above value cannot be beaten with three-party-correlation Bell inequalities.Comment: 7 page

Controlled and combined remote implementations of partially unknown quantum operations of multiqubits using GHZ states

We propose and prove protocols of controlled and combined remote implementations of partially unknown quantum operations belonging to the restricted sets [An Min Wang: PRA, \textbf{74}, 032317(2006)] using GHZ states. We detailedly describe the protocols in the cases of one qubit, respectively, with one controller and with two senders. Then we extend the protocols to the cases of multiqubits with many controllers and two senders. Because our protocols have to demand the controller(s)'s startup and authorization or two senders together working and cooperations, the controlled and combined remote implementations of quantum operations definitely can enhance the security of remote quantum information processing and potentially have more applications. Moreover, our protocol with two senders is helpful to farthest arrive at the power of remote implementations of quantum operations in theory since the different senders perhaps have different operational resources and different operational rights in practice.Comment: 26 pages, the submitted versio

Degree of entanglement as a physically ill-posed problem: The case of entanglement with vacuum

We analyze an example of a photon in superposition of different modes, and ask what is the degree of their entanglement with vacuum. The problem turns out to be ill-posed since we do not know which representation of the algebra of canonical commutation relations (CCR) to choose for field quantization. Once we make a choice, we can solve the question of entanglement unambiguously. So the difficulty is not with mathematics, but with physics of the problem. In order to make the discussion explicit we analyze from this perspective a popular argument based on a photon leaving a beam splitter and interacting with two two-level atoms. We first solve the problem algebraically in Heisenberg picture, without any assumption about the form of representation of CCR. Then we take the $\infty$-representation and show in two ways that in two-mode states the modes are maximally entangled with vacuum, but single-mode states are not entangled. Next we repeat the analysis in terms of the representation of CCR taken from Berezin's book and show that two-mode states do not involve the mode-vacuum entanglement. Finally, we switch to a family of reducible representations of CCR recently investigated in the context of field quantization, and show that the entanglement with vacuum is present even for single-mode states. Still, the degree of entanglement is here difficult to estimate, mainly because there are $N+2$ subsystems, with $N$ unspecified and large.Comment: This paper is basically a reply to quant-ph/0507189 by S. J. van Enk and to the remarks we got from L. Vaidman after our preliminary quant-ph/0507151. Version accepted in Phys. Rev.

Characterization of multiqubit pure-state entanglement

A necessary and sufficient entanglement criterion based on variances of Mermin-Klyshko's Bell operators is proved for multiqubit pure states. Contrary to Bell's inequalities, entangled pure states strictly satisfy a quadratic inequality but product ones can attain the equality under some local unitary transformations, which can be obtained by solving a quadratic maximum problem. This presents a characterization of multiqubit pure-state entanglement.Comment: 3 page

Substituting Quantum Entanglement for Communication

We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data is distributed among remote parties. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables one of them to learn the value of the function with only two bits of communication occurring among the parties, whereas, without quantum entanglement, three bits of communication are necessary. This result contrasts the well-known fact that quantum entanglement cannot be used to simulate communication among remote parties.Comment: 4 pages REVTeX, no figures. Minor correction

Contextuality in Measurement-based Quantum Computation

We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a super-polynomial speedup over the best known classical algorithm, namely the quantum algorithm that solves the Discrete Log problem.Comment: Version 3: probabilistic version of Theorem 1 adde

Proposed experiment for the quantum "Guess my number" protocol

An experimental realization of the entanglement-assisted "Guess my number" protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency eta > 0.70, which would require single photon detectors of efficiency sigma > 0.89. We propose a modification of the protocol which can be translated into a real experiment using present-day technology. In the proposed experiment, the quantum reduction of the multi-party communication complexity would require an efficiency eta > 0.05, achievable with detectors of sigma > 0.47, for four parties, and eta > 0.17 (sigma > 0.55) for three parties.Comment: REVTeX4, 4 pages, 1 figur

Demonstration of Temporal Distinguishability in a Four-Photon State and a Six-Photon State

An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multi-photon interference scheme in a recent discovered NOON-state projection measurement. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and thus quantitatively determine the degree of temporal (in)distinguishability of a multi-photon state

Production of multipartite entanglement for electron spins in quantum dots

We propose how to generate genuine multipartite entanglement of electron spin qubits in a chain of quantum dots using the naturally available single-qubit rotations and two-qubit Heisenberg exchange interaction in the system. We show that the minimum number of required operations to generate entangled states of the GHZ-, cluster and W-type scales linearly with the number of qubits and estimate the fidelities of the generated entangled cluster states. As the required single and two-qubit operations have recently been realized, our proposed scheme opens the way for experimental investigation of multipartite entanglement with electron spin qubits.Comment: 8 pages, 2 Figure

Nonlocal effects in Fock space

If a physical system contains a single particle, and if two distant detectors test the presence of linear superpositions of one-particle and vacuum states, a violation of classical locality can occur. It is due to the creation of a two-particle component by the detecting process itself.Comment: final version in PRL 74 (1995) 4571; 76 (1996) 2205 (erratum