(date 28. 02. 2021)

- Mark Hillery, Vladimír Bužek and André Berthiaume,
**Quantum secret sharing,**

Phys. Rev. A 59, 1829 – Published 1 March 1999 (2050 WOK citations)

https://doi.org/10.1103/PhysRevA.59.1829

Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using Greenberger-Horne-Zeilinger (GHZ) states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit. - D. R. Smith, S. Schultz, Peter Markoš, and C. M. Soukoulis
**Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients**

Phys. Rev. B 65, 195104 – Published 19 April 2002 (2024 WOK citations)

https://doi.org/10.1103/PhysRevB.65.195104

We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lengths of electromagnetic metamaterials, to determine the effective permittivity (ɛ) and permeability (μ). We perform this analysis on structures composed of periodic arrangements of wires, split ring resonators (SRRs), and both wires and SRRs. We find the recovered frequency-dependent ɛ and μ are entirely consistent with analytic expressions predicted by effective medium arguments. Of particular relevance are that a wire medium exhibits a frequency region in which the real part of ɛ is negative, and SRRs produce a frequency region in which the real part of μ is negative. In the combination structure, at frequencies where both the recovered real parts of ɛ and μ are simultaneously negative, the real part of the index of refraction is also found to be unambiguously negative. - Vladimír Bužek and Mark Hillery,
**Quantum copying: Beyond the no-cloning theore**

Phys. Rev. A 54, 1844 – Published 1 September 1996 (811 WOK citations)

https://doi.org/10.1103/PhysRevA.54.1844

We analyze the possibility of copying (that is, cloning) arbitrary states of a quantum-mechanical spin-1/2 system. We show that there exists a ‘‘universal quantum-copying machine’’ (i.e., transformation) which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input. We also examine a machine which combines a unitary transformation and a selective measurement to produce good copies of states in the neighborhood of a particular state. We discuss the problem of measurement of the output states. - Pranaw Rungta, Vladimír Bužek, Carlton M. Caves, Mark Hillery, and Gerard J. Milburn
**Universal state inversion and concurrence in arbitrary dimensions**

Phys. Rev. A 64, 042315 – Published 18 September 2001 (494 WOK citations)

doi.org/10.1103/PhysRevA.64.042315

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters’s concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a “universal inverter,” which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D1×D2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT superoperator. - M. S. Kim, W. Son, Vladimír Bužek, and Peter L. Knight
**Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement**

Phys. Rev. A 65, 032323 – Published 27 February 2002 (396 WOK citations)

doi.org/10.1103/PhysRevA.65.032323

A beam splitter is a simple, readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. We conjecture that this is a general property of beam splitters: Nonclassicality of the inputs is a necessary condition for entangling fields in a beam splitter. - Vladimír Bužek, A. Vidiella-Barranco, and Peter L. Knight
**Superpositions of coherent states: Squeezing and dissipation**

Phys. Rev. A 45, 6570 – Published 1 May 1992 (395 WOK citations)

doi.org/10.1103/PhysRevA.45.6570

In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping. - T. Koschny, Peter Markoš, D. R. Smith, and C. M. Soukoulis
**Resonant and antiresonant frequency dependence of the effective parameters of metamaterials**

Phys. Rev. E 68, 065602(R) – Published 15 December 2003 (361 WOK citations)

doi.org/10.1103/PhysRevE.68.065602

We present a numerical study of the electromagnetic response of the metamaterial elements that are used to construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an antiresonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus antiresonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the antiresonant behavior. - Jelena Klinovaja, Peter Stano, Ali Yazdani, and Daniel Loss
**Topological Superconductivity and Majorana Fermions in RKKY Systems**

Phys. Rev. Lett. 111, 186805 – Published 1 November 2013 (303 WOK citations)

https://doi.org/10.1103/PhysRevLett.111.186805

We consider quasi-one-dimensional Ruderman-Kittel-Kasuya-Yosida (RKKY) systems in proximity to an s-wave superconductor. We show that a 2kF peak in the spin susceptibility of the superconductor in the one-dimensional limit supports helical order of localized magnetic moments via RKKY interaction, where kF is the Fermi wave vector. The magnetic helix is equivalent to a uniform magnetic field and very strong spin-orbit interaction (SOI) with an effective SOI length 1/2kF. We find the conditions to establish such a magnetic state in atomic chains and semiconducting nanowires with magnetic atoms or nuclear spins. Generically, these systems are in a topological phase with Majorana fermions. The inherent self-tuning of the helix to 2kF eliminates the need to tune the chemical potential. - Vladimír Bužek, H. Moya-Cessa, Peter L. Knight, and S. J. D. Phoenix
**Schrödinger-cat states in the resonant Jaynes-Cummings model: Collapse and revival of oscillations of the photon-number distribution**

Phys. Rev. A 45, 8190 – Published 1 June 1992 (276 WOK citations)

https://doi.org/10.1103/PhysRevA.45.8190

The Jaynes-Cummings model of optical resonance describes the simplest fully quantized interaction between two quantum systems of different nature: a two-level atom (fermionic system) and a quantized field mode (bosonic system). This interaction leads to extreme quantum entanglement of the atom and field. However, the model also predicts that, at precisely half of the revival time, the atom and field become asymptotically disentangled. This disentanglement becomes more exact as the coherent-state amplitude increases. In this paper we investigate the nature of the pure-field-state superposition generated at such times. We show that this superposition is of distinguishable states of the field with the same amplitude but opposite phase. Interference between these components leads to nonclassical oscillations in photon-number distributions and squeezing in quadratures of the field. The Schrödinger-cat states of the field are highly transient, and depend very sensitively on the interaction time, the initial intensity of the field, and the atom-field detuning. - F. A. M. de Oliveira, M. S. Kim, Peter L. Knight, and Vladimír Bužek
**Properties of displaced number states**

Phys. Rev. A 41, 2645 – Published 1 March 1990 (249 WOK citations)

doi.org/10.1103/PhysRevA.41.2645

Recent developments in quantum optics have led to new proposals to generate number states of the electromagnetic field using conditioned measurement techniques or the properties of atom-field interactions in microwave cavities in the micromaser. The number-state field prepared in such a way may be transformed by the action of a displacement operator; for the microwave micromaser state this could be implemented by the action of a classical current that drives the cavity field. We evaluate some properties of such displaced number states, especially their description in phase space. The photon number distribution is shown to display unusual oscillations, which are interpreted as interference in phase space, analogous to Franck-Condon oscillations in molecular spectra. The possibility of detecting these oscillations is discussed, through the photodetection counting statistics of the displaced number states. We show that the displaced-number-state quantum features are relatively robust when dissipation of the field energy is included.