Entanglement conditions for two-mode states: Applications

Hillery, Mark; Zubairy, M. Suhail

doi:10.1103/physreva.74.032333

Cited by 117 publications

(78 citation statements)

References 33 publications

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“…(ii) Identifying some coefficients c nmkl leads to another way to formulate new conditions for NPT by reducing the number of independent variables of the form (12). For example, the quadratic form derived for the operatorf = c 1 +c 2â +c 3b depends on three independent (complex) variables c 1 , c 2 and c 3 .…”

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Inseparability Criteria for Continuous Bipartite Quantum States

2005

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We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under study. The violation of any inequality of this series is a sufficient condition for entanglement. Previously known entanglement conditions are shown to be special cases of our approach.PACS numbers: 03.67. Mn, 03.65.Ud, 42.50.Dv Entanglement plays a key role in the rapidly developing field of quantum information processing. In this context it is important to provide methods for characterizing entangled quantum states on the basis of observable quantities. However, already in seemingly simple cases this problem turns out to be rather complex. Even for a two-party harmonic-oscillator system so far there exists no complete characterization of entanglement to be used in experiments.For characterizing entanglement, that is inseparability, of the density operator of a bipartite continuous variable system, one may use the Peres-Horodecki condition [1,2,3]. A sufficient condition for entanglement consists in the negativity of the partial transposition (NPT) of the quantum state of the two-party system. To characterize NPT for such a system completely, however, to our best knowledge is still an unsolved problem.A sufficient condition for the NPT has been proposed by Simon [4]. It is based on second-order moments of position and momentum operators. For the special case of Gaussian states the resulting entanglement criterion has been shown to be necessary and sufficient. Another inseparability condition based on second moments has been derived without explicitely using the NPT condition [5]. This condition is also complete for the characterization of entanglement of two-mode Gaussian states. The latter approach has been extended to special higher-order moments [6,7] and even to more general operator functions [8].The complexity of the problem under study may become clear when we go back to a related but simpler problem. It consists in the characterization of nonclassical effects based on the negativity of the Glauber-Sudarshan P -function. Only recently the problem was solved of how to characterize the nonclassicality in terms of observable quantities. This requires an infinite hierarchy of conditions formulated either in terms of characteristic functions [9] or in terms of observable moments [10,11].In the present contribution we will further develop the concept of the complete characterization of single-mode nonclassicality with the aim to characterize the entanglement of bipartite continuous variable quantum states. Based on the NPT condition we derive a hierarchy of necessary and sufficient conditions for the NPT in terms of observable moments. Even though this only leads to sufficient conditions for entanglement, it can be applied to a variety of quantum states. It does not only contain as a special case the condition of Simon [4], but also other types of inequalities [5,6,7,8]. For ...

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“…c * pqrs c nmkl M pqrs,nmkl 0, (12) for the moments of the partial transposition M pqrs,nmkl = â †qâpâ †nâmb †sbrb †kbl PT .…”

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Inseparability Criteria for Continuous Bipartite Quantum States

2005

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“…Higher-order inequalities obtained from the Shchukin-Vogel criterion have been violated recently for a spatially non-Gaussian two-photon state which does not violate any second-order criteria [130]. We note that there exist several other CV entanglement criteria involving higher order moments [131,132,133,134,135,136,137,138,139,140,141].…”

Section: Continuous Variable Entanglement Criteriamentioning

confidence: 99%

Spatial correlations in parametric down-conversion

et al. 2010

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The transverse spatial effects observed in photon pairs produced by parametric down-conversion provide a robust and fertile testing ground for studies of quantum mechanics, non-classical states of light, correlated imaging and quantum information. Over the last 20 years there has been much progress in this area, ranging from technical advances and applications such as quantum imaging to investigations of fundamental aspects of quantum physics such as complementarity relations, Bell's inequality violation and entanglement. The field has grown immensely: a quick search shows that there are hundreds of papers published in this field, some with hundreds of citations. The objective of this article is to review the building blocks and major theoretical and experimental advances in the field, along with some possible technical applications and connections to other research areas.

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“…Since the system has three mode radiation modes, we take into account possibility of genuine three-mode entanglement. We use an extended set of mode correlation parameters [41] When any two of them become simultaneously positive, genuine three-mode entanglement is found. Typical example is the so called three parity W state [25] which is defined to be W = (|100 + |010 + |001 )/ √ 3.…”

Section: B Two Atomic Ensemblesmentioning

confidence: 99%

Quantum coherence and correlations of optical radiation by atomic ensembles interacting with a two-level atom in a microwave cavity

Müstecaplıoğlu

2011

Phys. Rev. A

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We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second order coherence degree, von Neumann entropy, spin squeezing for multi-particle entanglement, as well as genuine two and threemode entanglement parameters for steady state and non-equilibrium situations. Coherent transfer of population between the radiation modes and quantum state mapping between the two-level atom and the optical modes are discussed. A potential experimental realization of the theoretical results in a superconducting coplanar waveguide resonator containing diamond crystals with Nitrogen-Vacancy color centers and a superconducting artificial two-level atom is discussed.

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Entanglement conditions for two-mode states: Applications

Cited by 117 publications

References 33 publications

Inseparability Criteria for Continuous Bipartite Quantum States

Inseparability Criteria for Continuous Bipartite Quantum States

Spatial correlations in parametric down-conversion

Quantum coherence and correlations of optical radiation by atomic ensembles interacting with a two-level atom in a microwave cavity

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