Heralded noiseless linear amplification and distillation of entanglement

Xiang, Guo-Yong; Ralph, T. C.; Lund, Austin P.; Walk, Nathan; Pryde, Geoff J.

doi:10.1038/nphoton.2010.35

Cited by 330 publications

(377 citation statements)

References 26 publications

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“…Several implementations of non-Gaussian states have been reported so far, in particular from squeezed light [17][18][19][20][21][22][23][24][25], close-tothreshold parametric oscillators [26,27] in optical cavities [28], and in superconducting circuits [29]. Non-Gaussian operations are also interesting for tasks such as entanglement distillation [30,31] and noiseless amplification [32,33], which are also obtained in a conditional fashion, accepting only those events heralded by a measurement result.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

et al. 2010

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Non-Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non-Gaussianity of quantum states based on the conditional entropy of the state with a Gaussian reference. Here we adopt such a criterion to characterize an important class of nonclassical states: single-photon-added coherent states. Our studies demonstrate the reliability and sensitivity of this measure and use it to quantify how detrimental is the role of experimental imperfections in our implementation.

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Section: Introduction and Definitionsmentioning

confidence: 99%

Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

et al. 2010

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“…As an interesting feature, we are able to capture such nonclassical aspects at a glance. Our analysis first concerns the noiseless amplifier (Ĉ = gn, wherê n is the number operator and g > 1) [19,20]. We do not adopt a "black box" approach, but rather a model of the process is used so as to arrive at a description in term of generalized maps, also in the case when all the imperfections are taken into account.…”

Section: Example 1: the Noiseless Amplifiermentioning

confidence: 99%

“…Here we show, by a detailed physical model, the description of two conditioned processes which are relevant to continuous-variable state manipulation: the noiseless amplifier [19,20] and the single-photon addition [11,23]. We can derive the expression of the map in the well-known tensor form, and, as a step further, we illustrate a transfer function formalism, which allows us to describe the quantum process directly in the Wigner representation.…”

Section: Introductionmentioning

confidence: 99%

Heralded processes on continuous-variable spaces as quantum maps

et al. 2012

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Conditional evolution is crucial for generating non-Gaussian resources for quantum-information tasks in the continuous variable scenario. However, tools are lacking for a convenient representation of heralded processes in terms of quantum maps for continuous variable states, in the same way as Wigner functions are able to give a compact description of the quantum state. Here we propose and study such a representation, based on the introduction of a suitable transfer function to describe the action of a quantum operation on a Wigner function. We also reconstruct the maps of two relevant examples of conditional processes, that is, noiseless amplification and photon addition, by combining experimental data and a detailed physical model. This analysis allows us to fully characterize the effect of experimental imperfections in their implementations.

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“…However, if the state is unaccessible prior to phase encoding, we need to rely on operations which can enhance the amount of phase information already carried by the scrutinized state. Such operations are commonly referred to as noiseless amplifiers and a great deal of attention was recently devoted both to the concept [11] and to the experimental realizations [12]. The cost of this improvement comes in the reduced success rate of the operation.…”

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confidence: 99%

“…When discriminating quantum states drawn from a finite ensemble, one can accept existence of inconclusive results (reduced success rate) in order to reduce the probability of erroneous result to zero [13]. Similarly, when measuring a continuous parameter such as phase, it is possible to conditionally transform the quantum states in such the way that the subsequent measurement leads to more precise results [11,12]. Taken as whole, the combination of probabilistic operation and measurement is essentially a probabilistic measurement.…”

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confidence: 99%

Optimal probabilistic measurement of phase

Marek

2013

Phys. Rev. A

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When measuring phase of quantum states of light, the optimal single-shot measurement implements projection on the un-physical phase states. If we want to improve the precision further we need to accept a reduced probability of success, either by implementing a probabilistic measurement or by probabilistically manipulating the measured quantum state by means of noiseless amplification. We analyze the limits of this approach by finding the optimal probabilistic measurement which, for a given rate of success, maximizes the precision with which the phase can be measured.Phase is a central concept in both classical and quantum optics. It was, however, a matter of lengthy dialogue, before the quantum description of phase was established. The initial attempts of Dirac to treat phase as a canonical conjugate to photon number failed, because it is impossible to represent phase by a quantum mechanical observable [1]. As a consequence, phase can not be projectively measured, it can only be estimated (or guessed) by analyzing the results of other measurements. Despite this, phase states do exist [2] (even if they are not orthogonal) and they were eventually used to construct a well behaved phase operator [3]. Other attempts to describe phase properties of quantum states relied on the measurement-related phase distribution [4]. Both approaches were later reconciled with the fundamental canonical phase distribution [5].The canonical phase distribution characterizes phase properties of a quantum state and it is completely independent of its photon number distribution. It can be used to obtain a wide range of quantities related to phase estimation, but it also determines how much information about the phase of the state can be obtained by performing a measurement only on a single copy of it. True, the ideal canonical phase measurement does not and cannot exist, but several approximative approaches have been suggested [7,8].Aside from improving the actual detector scheme, overall performance of phase measurement can be also enhanced by specific alteration of the measured quantum state. Highly nonclassical quantum state can, in principle, lead to an unparalleled precision [9], while weakly nonclassical states are both beneficial and experimentally feasible [10]. However, if the state is unaccessible prior to phase encoding, we need to rely on operations which can enhance the amount of phase information already carried by the scrutinized state. Such operations are commonly referred to as noiseless amplifiers and a great deal of attention was recently devoted both to the concept [11] and to the experimental realizations [12]. The cost of this improvement comes in the reduced success rate of the operation. The amplification is therefore not very practical when the measurements can be repeated, but ut may be useful when the event to be detected is rare and we need to be certain that the single obtained measurement outcome corresponds to the theoretical value as closely as possible.However, even in the scenarios in which the probabili...

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Heralded noiseless linear amplification and distillation of entanglement

Cited by 330 publications

References 26 publications

Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

Heralded processes on continuous-variable spaces as quantum maps

Optimal probabilistic measurement of phase

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