Enhanced Communication with the Assistance of Indefinite Causal Order

Ebler, Daniel; Salek, Sina; Chiribella, Giulio

doi:10.1103/physrevlett.120.120502

Cited by 240 publications

(341 citation statements)

References 26 publications

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“…If the Kraus operators of the channels N 1 , N 2 and N 3 are {K (1) i }, {K (2) j } and {K (3) k } respectively, then the Kraus operators W ijk of the full quantum 3-switch channel is…”

Section: Tripartite Quantum Switchmentioning

confidence: 99%

Sending classical information via three noisy channels in superposition of causal orders

et al. 2020

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In this work, we study the transmission of classical information through three completely depolarizing channels in superposition of different causal orders. We thus introduce the quantum 3-switch as a resource for quantum communications. We perform a new kind of quantum control that was not accessible to the previously treated two-channel case. The fine and full quantum control achieved using selected combinations of causal orders let us uncover new features: non monotonous behavior on the transmission of information with respect to the number of causal orders involved, and different values of the transmission of information depending on the specific combinations of causal orders considered. Our results are a stepping stone to assess efficiency of coherent quantum control and optimize resources in the implementation of new indefinite causal structures. Finally, we suggest an optical implementation using standard telecom technology to test our predictions. operation known as quantum switch has been initially designed by Chiribella et al [9]. This primitive has subsequently been theoretically proposed as a novel resource for applications to quantum information theory [10,11], quantum communication complexity [12], quantum communication [2,13], non-local games [14] and quantum metrology [15,16]. Moreover, the quantum switch has been implemented experimentally [5,[17][18][19][20]. In the quantum switch, a target system ρ undergoes a superposition of two different causal orders of application of two quantum channels. A control system ρ c is used to route target system; the state ρ c = |1 1| encodes for order where channel one is applied before channel two while the state ρ c = |2 2| encodes for channel one after channel two. By placing ρ c in superposition, i.e. ρ c = |+ +|, where |+ c = 1 √ 2 (|1 +|2 ), ρ shall experience both orders simultaneously.

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“…If the Kraus operators of the channels N 1 , N 2 and N 3 are {K (1) i }, {K (2) j } and {K (3) k } respectively, then the Kraus operators W ijk of the full quantum 3-switch channel is…”

Section: Tripartite Quantum Switchmentioning

confidence: 99%

Sending classical information via three noisy channels in superposition of causal orders

et al. 2020

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“…Let us assume now that  1 and  2 cover the full set  , so that    È = constraints: 1 here, and that its complete positiveness is in fact irrelevant) 11 . We thus equivalently have the following characterisation:…”

Section: A2 Compatibility With Fixed Causal Ordersmentioning

confidence: 99%

On the definition and characterisation of multipartite causal (non)separability

2019

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The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined global causal structure. While the definition is unambiguous in the bipartite case, its generalisation to the multipartite case is not so straightforward. Two seemingly different generalisations have been proposed, one for a restricted tripartite scenario and one for the general multipartite case. Here we compare the two, showing that they are in fact inequivalent. We propose our own definition of causal (non)separability for the general case, which-although a priori subtly different -turns out to be equivalent to the concept of 'extensible causal (non)separability' introduced before, and which we argue is a more natural definition for general multipartite scenarios. We then derive necessary, as well as sufficient conditions to characterise causally (non)separable processes in practice. These allow one to devise practical tests, by generalising the tool of witnesses of causal nonseparability. J Wechs et ali.e. the unitaries are applied in a 'superposition of orders'. The output state is then sent to a third party C (Charlie) who can measure the control qubit, and possibly also the target system. The protocol just described can straightforwardly be generalised to the case where A and Bʼs operations are general quantum instruments instead of unitaries. This so-called quantum switch can be understood as a quantum supermap [23], or higher order transformation, that maps A and Bʼs local operations to the overall global transformation. It cannot be realised by inserting the local operations into a circuit with a well-defined causal order, and therefore constitutes a new resource for quantum computation that goes beyond causally ordered quantum circuits [4]. It has attracted particular interest as a consequence of being readily implementable, and indeed several implementations have been experimentally realised [24-28]. Consequent work has sought to clarify whether such implementations can New J. Phys. 21 (2019) 013027 J Wechs et al New J. Phys. 21 (2019) 013027 J Wechs et al 12 1 2 (which may be empty), respectively, one must have 18 New J. Phys. 21 (2019) 013027 J Wechs et al W k M k 1 1 is causally separable. 30 New J. Phys. 21 (2019) 013027 J Wechs et al

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“…Having transverse spatial modes as the target d.o.f. enables encoding qudits-as opposed to qubits-for investigating quantum communication with indefinite causal order in larger Hilbert space dimensions [5,8]. The benefits of using qudits for quantum information processing applications, such as improved security in quantum cryptography and higher information capacity in quantum communication, are well known [33,34].…”

Section: -3mentioning

confidence: 99%

“…Strikingly, it has been proposed that quantum physics allows for nonclassical causal structures where the order of events is indefinite [1,2]. It has been theoretically shown that such a possibility provides an advantage for computation [3], communication complexity [4,5], and other information processing tasks [6][7][8]. Furthermore, investigations of indefinite causal orders suggest a promising route towards a theory that combines general relativity and quantum mechanics [9,10].…”

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confidence: 99%

Indefinite Causal Order in a Quantum Switch

et al. 2018

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Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operationsÂ andB act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound. DOI: 10.1103/PhysRevLett.121.090503 In daily experience, it is natural to think of events happening in a fixed causal order. Strikingly, it has been proposed that quantum physics allows for nonclassical causal structures where the order of events is indefinite [1,2]. It has been theoretically shown that such a possibility provides an advantage for computation [3], communication complexity [4,5], and other information processing tasks [6][7][8]. Furthermore, investigations of indefinite causal orders suggest a promising route towards a theory that combines general relativity and quantum mechanics [9,10].Indefinite causal orders can be studied using a framework that distinguishes whether some experimental situationcalled a "process"-is compatible with a fixed causal order of the events or not. An example of a process with indefinite causal order is the "quantum switch" [1]. In the quantum switch, the order in which two quantum operationÂ andBconsidered as "black box operations"-are performed on a target system is coherently controlled by a control quantum system (Fig. 1). This can also be seen as a particular case of "superposition of time evolution" [11]. The advantages provided by the quantum switch arise from the fact that it cannot be reproduced by an ordinary quantum circuit which uses the same number of black box operations [3][4][5][6][7].Here, we present an optical implementation of the quantum switch where the control system is the photon's polarization and the target is the transverse spatial mode. We verify indefinite causal order by introducing a causal witness [14,15], for which we obtain a value 18 standard deviations beyond the bound for definite ordering. One notable achievement of our experiment is that it opens the possibility of encoding more than two levels in the target system-transverse spatial mode can indeed be highdimensional and hence can act as a qudit.In previous implementations [12,13], the location of each black box-the spot where photons go through a set of wave plates-was different depending on the order, resulting in four distinct locations in space [ Fig. 1(c)]. Furthermore, the photons had a coherence length much shorter than the distance between the two sets of wave plates: in effect, the operations could also be distinct in...

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Enhanced Communication with the Assistance of Indefinite Causal Order

Cited by 240 publications

References 26 publications

Sending classical information via three noisy channels in superposition of causal orders

Sending classical information via three noisy channels in superposition of causal orders

On the definition and characterisation of multipartite causal (non)separability

Indefinite Causal Order in a Quantum Switch

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