Classical communication cost of quantum steering

Sainz, Ana Belén; Aolita, Leandro; Brunner, Nicolás; Gallego, Rodrigo; Skrzypczyk, Paul

doi:10.1103/physreva.94.012308

Cited by 19 publications

(21 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These are extremal in the sense that they cannot be obtained from other singlet assemblages via 1WLOCC [12]. Furthermore, they are known to maximize important measures of quantum steering [3,13,14]. In particular, we consider the singlet assemblage Σ Φ + A|X obtained from the maximally entangled state |Φ + := (|00 + |11 )/ Alice can only perform uncharacterized measurements on her device, which is then effectively treated as a black box.…”

mentioning

confidence: 99%

Distillation of Quantum Steering

et al. 2020

View full text Add to dashboard Cite

We show -both theoretically and experimentally -that Einstein-Podolsky-Rosen steering can be distilled. We present a distillation protocol that -in the asymptotic infinite-copy limit -outputs a perfect singlet assemblage even for inputs that are arbitrarily close to being unsteerable. As figures of merit for the protocol's performance, we introduce the assemblage fidelity and the singlet-assemblage fraction. These are potentially interesting quantities on their own beyond the current scope. Remarkably, the protocol works well also in the non-asymptotic regime of few copies, in the sense of increasing the singlet-assemblage fraction. We demonstrate the efficacy of the protocol using a hyperentangled photon pair encoding two copies of a two-qubit state. This represents to our knowledge the first observation of deterministic steering concentration. Our findings are not only fundamentally important but may also be useful for semi device-independent protocols in noisy quantum networks.Steering is a unique form of quantum nonlocality that appears in hybrid quantum networks with both trusted and untrusted components [1]. These scenarios are referred to as semi device-independent (DI), in contrast to the fully DI context, where all apparatuses are untrusted, or the devicedependent one, with trusted components exclusively. A trusted device allows for full quantum control of the system it operates, e.g. through well-characterized quantum measurements on it. A device is untrusted if one can only control its classical settings (inputs), obtaining classical outcomes (outputs) of uncharacterised measurements from it, thus effectively working as a black-box device. Importantly, steering certifies the presence of entanglement in a semi-DI fashion. Due to this, apart from its fundamental relevance, it is important also from an applied point of view: Steering is known to be the key resource behind several information-processing tasks in the semi-DI scenario [2,3].However, as experimental quantum networks grow ever more complex, the unavoidable noise and imperfections become increasingly significant. This can severely degrade the steering in the network, compromising the performance of the implemented task. Distillation protocols are ideal for these situations, as they concentrate the resource contained in multiple copies of a noisy system into a pure maximallyresourceful system, which can then be directly used safely for the task in question. Interestingly, distillation protocols are known for the other two paradigmatic variants of quantum nonlocality-namely, entanglement in the devicedependent framework and Bell nonlocality in the fully DI one- [4,5] and also even for other important quantum resources [6][7][8][9][10][11]. Nevertheless, to our knowledge, nothing is known for the case of steering. In particular, it is neither known whether steering distillation exists (in the asymptotic regime of infinitely many copies of the noisy system) or even if steering can be partially purified in the finite-copy regime.Here, we answer both...

show abstract

mentioning

confidence: 99%

Distillation of Quantum Steering

et al. 2020

View full text Add to dashboard Cite

show abstract

“…One candidate task is entanglement-assisted sub-channel discrimination with oneway measurements [38], where it is known that it is steering, rather than simple entanglement [57], that gives an advantage. Post-quantum steering might also help trivialise certain communication tasks (see [58]). We leave it for future work whether post-quantum steering is more useful for any of these tasks, and whether the formalism introduced here might facilitate the study of this question.…”

Section: Discussionmentioning

confidence: 99%

A formalism for steering with local quantum measurements

et al. 2018

View full text Add to dashboard Cite

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models, which will be defined in this work. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.The concept of steering was first introduced by Schrödinger in 1935 [1] in response to the Einstein et al paradox [2]. It refers to the phenomenon where one party, Alice, by performing measurements on one part of a shared system, seemingly remotely 'steers' the state of the system held by a distant party, Bob, in a way which has no explanation in terms of local causal influences. Steering has only recently been formally defined in a quantum information-theoretic setting [3], as a way of certifying the entanglement of quantum systems without the need to trust one of the parties, or when one of the parties is using uncharacterised devices. In this setting, the uncharacterised party convinces the other party that they shared entanglement by demonstrating steering. Furthermore, if all parties are uncharacterised (or untrusted) then one recovers the device-independent setting of a standard Bell test. Steering thus may be seen as one in a family of non-classical phenomena, closely related to entanglement and Bell non-locality [4]. Indeed, Bell nonlocality implies steering, and steering implies entanglement, however all three concepts are inequivalent [3,5].It is well-known that, in spite of demonstrating non-locality, local measurements on entangled quantum systems cannot be used to communicate superluminally. That is, correlations that are generated by varying the choice of local measurements on space-like separated quantum subsystem-which we define to be quantum correlations-satisfy the principle of no-signalling. We will call no-signalling colleations all correlations that do not permit signalling. One can conceive of no-signalling correlations that cannot be realised by local measurements on quantum states, hence called post-quantum correlations; this possibility was first pointed out in a seminal work...

show abstract

“…In order to satisfy the 1st and 4th row given in Eq. (32), the only possible choice for P(b|y, ρ 0 ) and P(b|y, ρ 1 ) are: (39) and P(b|y,…”

Section: A Super-unsteerability: Examplementioning

confidence: 99%

“…On the other hand, quantum nonlocality and steering are also associated with incompatibility of measurements [34][35][36][37]. From an operational perspective, nonlocal or steerable states require pre-shared randomness with non-zero communication cost [38,39]. Here we are concerned with the question of how to give such an operational characterization to the quantumness of local or unsteerable correlations.…”

Section: Introductionmentioning

confidence: 99%

Operational characterization of quantumness of unsteerable bipartite states

et al. 2018

View full text Add to dashboard Cite

Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A 95, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as super-correlation, the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be super-correlated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of super-unsteerability, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories. * debarshidas@jcbose.ac.in †

show abstract

Classical communication cost of quantum steering

Cited by 19 publications

References 35 publications

Distillation of Quantum Steering

Distillation of Quantum Steering

A formalism for steering with local quantum measurements

Operational characterization of quantumness of unsteerable bipartite states

Contact Info

Product

Resources

About