Experimental determination of entanglement with a single measurement

Walborn, S. P.; Ribeiro, P. H. Souto; Davidovich, L.; Mintert, Florian; Buchleitner, Andreas

doi:10.1038/nature04627

Cited by 329 publications

(350 citation statements)

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“…Moreover, the recent proposals to directly measure the dissipative entanglement evolution have opened up a possibility of experimentally demonstrating the onset of the non-additivity when nonlocal coherence decay is concerned [27,29].…”

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confidence: 99%

Quantum Open System Theory: Bipartite Aspects

2006

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We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.PACS numbers: 03.65. Yz, 03.65.Ud, 42.50.Lc In this note we will establish results that contradict the long-standing belief that additivity of coherence decay rates is a natural consequence of weak noises. This belief means that the relaxation rate of any system exposed to a collection of weak noises is the sum of the relaxation rates associated with the noises separately. Although implied in many textbook discussions, an actual proof of additivity may be difficult to locate. We supply here a proof of additivity for a single qubit coupled to two independent weak noises (here amplitude noise and phase noise), but our main message is the demonstration of violations of additivity in the case of entanglement decay when two or more qubits are involved. That is, we will show that a quantum system with the most elementary composite structure (e.g., simply made of two distinct parts) need not and generally does not exhibit relaxation-rate additivity even though the separate parts do. This result is purely quantum mechanical and extends our understanding of the power of quantum coherence in an unexpected direction.We now present an additivity proof that is quantum mechanical in order to eliminate from concern the possibility that quantum systems are intrinsically different from classical ones in their response to weak noise. We will consider ideal noise sources where "ideal" means that the noise is sufficiently weak and random that the noisesystem interaction is both reliably linear and without significant back action on the noise source. Each noise source can then be treated as a reservoir made of an infinite collection of random and very broadband harmonic oscillators at zero temperature.Of course the relaxing system need not be linear, so we choose the simplest nonlinear system, a qubit (two-level atom, spin one-half, etc.), for our example. The total Hamiltonian for a qubit coupled to two noise sources (two "environments") can be written as follows:(1) * Electronic address: ting@pas.rochester.edu † Electronic address: eberly@pas.rochester.edu where (with = 1)are the Hamiltonians of the qubit system and two local environments. As an example of the types of relaxation that will be relevant, we suppose the two environments couple in the one case longitudinally and in the other case transversely to the qubit. Thus we have for the interaction of the qubit with its two different noise sources:We naturally assume that the two noise sources are not cross-correlated, and in the ideal case under consideration they can be treated in the familiar Born-Markov limit. Thus we write the longitudinal and transverse selfcorrelation functions in the...

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confidence: 99%

Quantum Open System Theory: Bipartite Aspects

2006

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“…In particular, somewhat surprisingly, it was shown how to estimate and/or even measure amount of entanglement (concurrence) without prior state reconstruction [11,12,13]. Recently the method got the new twist thanks to application of such collective measurements [20,21,22,23] that are directly related to quantum concurrence (see [24]) including photon polarization-momentum experimental demonstration for pure states in distant laboratories paradigm [20]. Recently collective entanglement witnesses were also shown to lead to easily measurable lower bounds on entanglement [21].…”

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Universal observable detecting all two-qubit entanglement and determinant-based separability tests

2008

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We construct a single observable measurement of which mean value on four copies of an unknown two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal collective entanglement witness detecting all two-qubit entanglement. The test is directly linked to a function which characterizes to some extent the entanglement quantitatively. This function is an entanglement monotone under so-called local pure operations and classical communication (pLOCC) which preserve local dimensions. Moreover it provides tight upper and lower bounds for negativity and concurrence. Elementary quantum computing device estimating unknown two-qubit entanglement is designed.PACS numbers: 03.65.-wIntroduction .-One of the main challenges of both theoretical and experimental Quantum Information Theory is a determination of entanglement properties of a given state. There is an extensive literature covering the problem of deciding entanglement of a state [1,2,3,4,5,6,7]. As one knows from the seminal paper of Peres and Wootters [8] collective measurement on several copies of a system in a given quantum state may provide better results than measurements performed on each copy separately. This fact was reflected in the method of entanglement detection with collective measurements. The method initiated for pure states [9, 10], then developed for mixed states with help of quantum networks [11,12,13,14,15,16,17] and the concept of collective entanglement witnesses [18], has found its first experimental demonstration in coalescence-anti coalescence coincidence experiment [19]. In particular, somewhat surprisingly, it was shown how to estimate and/or even measure amount of entanglement (concurrence) without prior state reconstruction [11,12,13]. Recently the method got the new twist thanks to application of such collective measurements [20,21,22,23] that are directly related to quantum concurrence (see [24]) including photon polarization-momentum experimental demonstration for pure states in distant laboratories paradigm [20]. Recently collective entanglement witnesses were also shown to lead to easily measurable lower bounds on entanglement [21]. The idea of collective entanglement witnesses was also implemented in continuous variables setup [22].We show that a single observable if measured on four copies of a unknown two-qubit state is sufficient for discrimination between entanglement and separability of it. Moreover it can serve for limited quantitative purposes. To this aim we explore the two-qubit separability test (equivalent to the PPT one [2,25]) stating that a state is separable iff the determinant of its partially transposed density matrix is nonnegative [26,27]. The result, known for a few years, was barely mentioned in the literature in that form (see e.g. [28]) and up to our knowledge this is the first time an operative physical meaning is assigned

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“…An alternative route to enhance the size of a system is through hyperentanglement [8], that is, the entanglement in multiple degrees of freedom (DOF) of a composite quantum system. So far, hyperentanglement has found use in high-capacity quantum communication [9][10][11][12][13], photonic quantum computing [14,15], tests of quantum non-locality [16,17], and the direct characterization of entanglement [18] and quantum dynamics [19]. Here we demonstrate the usefulness of hyperentanglement in metrology, allowing one to reach the ultimate quantum precision limits, for the paradigmatic case of an interaction between two degrees of freedom of the same system.…”

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confidence: 67%

Quantum-enhanced sensing from hyperentanglement

Walborn

Filho

2018

Phys. Rev. A

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Hyperentanglement -simultaneous entanglement between multiple degrees of freedom of two or more systems -has been used to enhance quantum information tasks such as quantum communication and photonic quantum computing. Here we show that hyperentanglement can lead to increased quantum advantage in metrology, with contributions from the entanglement in each degree of freedom, allowing for Heisenberg scaling in the precision of parameter estimation. Our experiment employs photon pairs entangled in polarization and spatial degrees of freedom to estimate a small tilt angle of a mirror. Precision limits beyond shot noise are saturated through a simple binary measurement of the polarization state. The broad validity of the dynamics considered here implies that similar strategies based on hyperentanglement can offer improvement in a wide variety of metrological tasks.To exploit the advantage of quantum entanglement for tasks such as computation and metrology requires producing highdimensional quantum states composed of many entangled sub-systems [1][2][3][4]. In addition to the difficulty in producing large entangled states, they are typically very sensitive to noise [5][6][7]. An alternative route to enhance the size of a system is through hyperentanglement [8], that is, the entanglement in multiple degrees of freedom (DOF) of a composite quantum system. So far, hyperentanglement has found use in high-capacity quantum communication [9][10][11][12][13], photonic quantum computing [14,15], tests of quantum non-locality [16,17], and the direct characterization of entanglement [18] and quantum dynamics [19]. Here we demonstrate the usefulness of hyperentanglement in metrology, allowing one to reach the ultimate quantum precision limits, for the paradigmatic case of an interaction between two degrees of freedom of the same system. Examples of this type of evolution include the interaction between spin and momentum in a SternGerlach experiment, between internal and external DOF of trapped ions [20], or the polarization and spatial DOF of an optical field propagating through a birefringent medium [21].Our experiment employs hyperentangled photon pairs to monitor a tiny rotation of a mirror. Entanglement in both spatial and polarization DOF leads to increased quantum advantage in metrological sensing, allowing for Heisenberg scaling in the number of photons N used to probe the rotation: the precision of estimation becomes proportional to 1/N , instead of the shot-noise behavior ∝ 1/ √ N . Estimation of tilt angles of mirrors is important in several fields of science [22][23][24][25]. A common procedure consists in detecting the spatial or phase displacement of a laser beam reflected by the mirror [26][27][28][29][30][31][32]. Our method, on the other hand, is based solely on a binary polarization measurement at the output of an interferometer with a displaced input beam. This scheme takes advantage of both hyper-entanglement and beam displacement to increase the precision beyond the shot-noise limit.Precision measurements and F...

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Experimental determination of entanglement with a single measurement

Cited by 329 publications

References 20 publications

Quantum Open System Theory: Bipartite Aspects

Quantum Open System Theory: Bipartite Aspects

Universal observable detecting all two-qubit entanglement and determinant-based separability tests

Quantum-enhanced sensing from hyperentanglement

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