Measurement-device-independent entanglement and randomness estimation in quantum networks

Šupić, Ivan; Skrzypczyk, Paul; Cavalcanti, Daniel

doi:10.1103/physreva.95.042340

Cited by 45 publications

(57 citation statements)

References 69 publications

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“…Given a bipartition S S N 1, ..., 1 2 If a distributed measurement is non-signalling but not quantum then we refer to this as post-quantum Buscemi non-locality. We are not the first to describe the set of non-signalling distributed measurements, Šupić et al [35] defined this set in the bipartite setting, although the terminology 'distributed measurement' is of our creation. We believe we are, however, the first to point out the possibility of post-quantum Buscemi nonlocality.…”

Section: Definition 20mentioning

confidence: 99%

A channel-based framework for steering, non-locality and beyond

Hoban

Sainz

2018

New J. Phys.

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Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, 'post-quantum steering' has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin-Hughston-Jozsa-Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon.Entanglement is one of the most striking non-classical features of quantum mechanics. Given appropriately chosen measurements certain, but not all, entangled states can exhibit a violation of local realism (local causality), called 'non-locality' [1]. Apart from its fundamental interest, non-locality has also turned into a key resource for certain information-theoretic tasks, such as key distribution [2] or certified quantum randomness generation [3], and has been witnessed experimentally in a loophole-free manner [4][5][6].The non-classical implications of entanglement also manifest as a phenomenon called 'Einstein-Podolsky-Rosen steering', henceforth referred to as solely 'steering'. There, one party, Alice, by performing appropriately chosen measurements on one half of an entangled state, remotely 'steers' the states held by a distant party, Bob, in a way which has no local explanation [7]. A modern approach to steering describes it as a way to certify entanglement in cryptographic situations where some devices in the protocol are not characterized [8]. Steering hence allows for a 'one-sided device-independent' implementation of several information-theoretic tasks, such as quantum key distribution [9], randomness certification [10,11], measurement incompatibility certification [12][13][14], and self-testing of quantum states [15,16].Even though these phenomena arise naturally within quantum mechanics, they are not restricted to it. Non-local correlations and steering beyond what quantum theory allows are conceivable while still complying with natural physical assumptions, such as relativistic causality [17,18]. By 'post-quantum' we m...

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Section: Definition 20mentioning

confidence: 99%

A channel-based framework for steering, non-locality and beyond

Hoban

Sainz

2018

New J. Phys.

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“…Consequently, we argue that ℘ MDI NPT is computable using convex optimization algorithms in almost all cases of interest. Following Brandão [14] and Eisert et al [15], in this particular case, our measure provides a MDI lower bound on the amount of random robustness, [13] that is the minimum amount of white noise to be added to the effective entangled stateς A 0 B 0 so that all the entanglement is removed [46].…”

Section: An Extremal Ew (Eew)ŵmentioning

confidence: 99%

Measurement-Device-Independent Approach to Entanglement Measures

2017

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Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states. DOI: 10.1103/PhysRevLett.118.150505 Introduction.-Entanglement is a valuable resource for practical as well as fundamental applications of quantum theory, ranging from quantum computation and communication to metrology [1-3]. There are two major challenges in understanding entanglement that stimulates this research. First, it is extremely difficult to specify all the nonentangled bipartite or multipartite quantum states. In fact, the problem is known to be NP-hard [4,5]. Second, not surprisingly, the characterization of entangled states, i.e., the quantification of entanglement within quantum states, is an equally difficult task. The answer to the second challenge is practically very important because it tells us how well our protocols will perform using a given state [6][7][8][9].Focusing on the second challenge above, a first level of hardness is that the quantification of entanglement using almost any entanglement measure, e.g., entanglement of formation [10], negativity [11,12], or random robustness [13], requires estimating a large number of density matrix elements, a task which is difficult to perform on bipartite and multipartite quantum states. While this difficulty can be partially circumvented by making use of entanglement witnesses (EWs) when lower bounds on the entanglement are desired [14][15][16][17][18][19], errors and misalignments of the measurement devices can still lead to incorrect estimations of the quantities and thus, erroneous conclusions. A measurementdevice-independent approach is therefore desirable.Recent work by Buscemi [20] has introduced a new way to think about entanglement detection [21][22][23][24]. The idea is to map the problem onto a modified class of nonlocal games, called semiquantum nonlocal games (SQNLGs). In any such game, two players (Alice and Bob) share a possibly entangled state. A referee (Charlie) starts by asking them

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“…Some of these tests have been implemented experimentally [44][45][46][47]; and even when no prior knowledge about the tested systems is available, the verification can be performed directly on experimental data [47][48][49]. Within this framework, several authors proposed structural or quantitative tests of entanglement [49][50][51][52] or the quantification of generated randomness [52][53][54]. In our construction below, we apply the MDI framework to temporal correlations arising out of the use of a quantum memory.…”

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confidence: 99%

Resource Theory of Quantum Memories and Their Faithful Verification with Minimal Assumptions

2018

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We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially). As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non entanglement-breaking channel can be certified. Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification. As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted. An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.Consider a vendor selling quantum devices purportedly able of storing quantum information for a period of time. However, during their operation, the devices always break the entanglement between the stored subsystem and any other subsystem. Such devices are arguably useless as quantum memories; for example, they would not be able to establish entangled links in a quantum repeater scheme [1,2]. In the terminology of quantum channels [3][4][5], those devices correspond to entanglementbreaking (EB) channels [6,7], which are exactly equivalent to the measure-and-prepare channels depicted in Fig. 1. Measure-and-prepare channels are implemented by measuring the input state, storing the classical information corresponding to the measurement outcome for the required duration, and then using that information to prepare a quantum state. Even though strictly speaking, such channels are quantum channels (since they act upon an input quantum system), they actually transmit only classical information from the input to the output. Thus, in constructing a quantum memory, one aims to produce a device that could retain some correlations between the stored system and remote systems.Due to its relevance in quantum information science, the benchmarking of quantum memories has been extensively considered in the literature [8][9][10][11][12]. An obvious way to verify whether a channel is EB or not is by performing process tomography [13][14][15], that is, by feeding through the channel a tomographically complete set of states and performing a tomographically complete measurement at the output. By collecting sufficient statistics, it is possible to reconstruct the process matrix corresponding to the channel up to any desired level of accuracy, and check whether the channel is EB or not. This scheme, however...

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Measurement-device-independent entanglement and randomness estimation in quantum networks

Cited by 45 publications

References 69 publications

A channel-based framework for steering, non-locality and beyond

A channel-based framework for steering, non-locality and beyond

Measurement-Device-Independent Approach to Entanglement Measures

Resource Theory of Quantum Memories and Their Faithful Verification with Minimal Assumptions

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