Preparation of distilled and purified continuous-variable entangled states

Hage, B.; Samblowski, Aiko; DiGuglielmo, James; Franzen, A.; Fiurášek, Jaromı́r; Schnabel, R.

doi:10.1038/nphys1110

Cited by 98 publications

(96 citation statements)

References 31 publications

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“…However, the distance over which quantum states of light can be distributed without significant disturbance is limited due to unavoidable losses and noise in optical links. Losses, as well as errors or decoherence, may in principle be overcome by the sophisticated techniques of quantum error correction [2][3][4], entanglement distillation [5][6][7], and quantum repeaters [8,9]. However, these techniques typically require encoding information into complex multimode entangled states, processing many copies of an entangled state, and -even more challenging -using quantum memories [10,11].…”

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Noiseless Loss Suppression in Quantum Optical Communication

et al. 2012

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We propose a protocol for conditional suppression of losses in direct quantum state transmission over a lossy quantum channel. The method works by noiselessly attenuating the input state prior to transmission through a lossy channel followed by noiseless amplification of the output state. The procedure does not add any noise hence it keeps quantum coherence. We experimentally demonstrate it in the subspace spanned by vacuum and single-photon states, and consider its general applicability.PACS numbers: 03.67. Hk, 42.50.Ex Quantum communication holds the promise of unconditionally secure information transmission [1]. However, the distance over which quantum states of light can be distributed without significant disturbance is limited due to unavoidable losses and noise in optical links. Losses, as well as errors or decoherence, may in principle be overcome by the sophisticated techniques of quantum error correction [2][3][4], entanglement distillation [5][6][7], and quantum repeaters [8,9]. However, these techniques typically require encoding information into complex multimode entangled states, processing many copies of an entangled state, and -even more challenging -using quantum memories [10,11]. In stark contrast with the situation for classical communication, losses in quantum communication cannot be compensated by amplifying the signal, because the laws of quantum mechanics imply that any deterministic phase-insensitive signal amplification is unavoidably accompanied by the addition of noise [12].Very recently, however, the concept of heralded noiseless amplification of light [13] was proposed as a way out, relaxing the deterministic requirement. The noiseless amplification is formally described by a quantum filter g n , where n is the photon number operator and g > 1 denotes the amplification gain. The noiseless amplifier thus modulates amplitudes of Fock states |n by factor g n . This filtration can conditionally increase amplitude of a coherent state |α without adding any noise, g n |α ∝ |gα . Although this cannot be done perfectly because g n is unbounded, faithful noiseless amplification is possible in any finite subspace spanned by the Fock states |n with n ≤ N , albeit with a correspondingly low probability scaling as g −2N in the worst case of input vacuum state. With current technology, it has been proven possible to faithfully noiselessly amplify weak coherent states containing mostly vacuum and single-photon contributions [14][15][16][17].The noiseless amplifier can improve the performance of quantum key distribution protocols [18][19][20][21] and it can also be used to distribute high-quality entanglement over a lossy channel [13,22]. Beyond that, the noiseless amplifier is not useful to suppress losses in direct transmission of arbitrary quantum states because it is not the inverse map of a lossy channel L. As a matter of fact, any superposition of Fock states that is not a coherent state is mapped by L onto a mixed state, and this added noise cannot be eliminated by noiseless amplification.He...

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Noiseless Loss Suppression in Quantum Optical Communication

et al. 2012

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“…Purification of two mode entangled states has been shown experimentally for qubits [20,21] and in the continuous variable (CV) regime [22,23]. (CV-entanglement purification is especially challenging [24][25][26].…”

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Quantum state engineering, purification, and number-resolved photon detection with high-finesse optical cavities

et al. 2010

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We propose and analyze a multi-functional setup consisting of high finesse optical cavities, beam splitters, and phase shifters. The basic scheme projects arbitrary photonic two-mode input states onto the subspace spanned by the product of Fock states |n |n with n = 0, 1, 2, . . .. This protocol does not only provide the possibility to conditionally generate highly entangled photon number states as resource for quantum information protocols but also allows one to test and hence purify this type of quantum states in a communication scenario, which is of great practical importance. The scheme is especially attractive as a generalization to many modes allows for distribution and purification of entanglement in networks. In an alternative working mode, the setup allows of quantum non demolition number resolved photodetection in the optical domain.

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“…Non-Gaussian operations are required for entanglement distillation or swapping (4)(5)(6)(7)(8), and their use along with non-Gaussian states has been shown to improve quantum teleportation (9, 10) and cloning (11). It is also particularly remarkable that non-Gaussianity (either states or operations) is necessary for universal quantum computation with CVs (12), and proof of quantum nonlocality through violation of Bell's inequality (13).…”

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Quantum entanglement beyond Gaussian criteria

Gomes

Salles

Toscano

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states.continuous variables | quantum information | non-Gaussian states | transverse spatial modes S ince the realization that quantum systems could prove useful for the efficient processing of information, there have appeared many proposals designed to exploit their power. From database searching and factoring algorithms to secure communication, these protocols achieve an impressive range of tasks. Typically, these quantum protocols have been first designed for discrete variable systems, described by finite dimensional Hilbert spaces, and hence are mathematically simpler than continuous variable (CV) systems with infinite dimensional spaces (1). CV systems provide a very interesting ground for quantum information processing, precisely due to their large and rich Hilbert space structure, which, however, makes characterization and detection of CV entanglement a difficult task.One way to tackle the difficulty in dealing with infinite dimensions is to confine the allowed states to a sector of Hilbert space defined by a finite number of parameters. Among the infinite ways one could do this, the most common is to restrict oneself to Gaussian states. For zero mean values, these states can be completely characterized by their covariance matrix containing moments up to second order (e.g. x 2 , xp , etc.) (1). This simplification has allowed for many results from the realm of finite-dimensional discrete-variable entanglement to find their CV analog (2, 3).It has recently become apparent, however, that the use of non-Gaussian states and operations is not only advantageous but at times necessary to successfully perform quantum information tasks. Non-Gaussian operations are required for entanglement distillation or swapping (4-8), and their use along with non-Gaussian states has been shown to improve quantum teleportation (9, 10) and cloning (11). It is also particularly remarkable that non-Gaussianity (either states or operations) is necessary for universal quantum computation with CVs (12), and proof of quantum nonlocality through violation of Bell's inequality (13). These advantages have motivated the experimental de-Gaussification of Gaussian states (14-17) and the idea that non-Gaussianity is a resource that can be quantified (18).The most popular criteria for identifying CV entanglement deal with mom...

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Preparation of distilled and purified continuous-variable entangled states

Cited by 98 publications

References 31 publications

Noiseless Loss Suppression in Quantum Optical Communication

Noiseless Loss Suppression in Quantum Optical Communication

Quantum state engineering, purification, and number-resolved photon detection with high-finesse optical cavities

Quantum entanglement beyond Gaussian criteria

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