Quantum Shannon theory with superpositions of trajectories

Chiribella, Giulio; Kristjánsson, Hlér

doi:10.1098/rspa.2018.0903

Cited by 114 publications

(158 citation statements)

References 52 publications

Supporting

Mentioning

148

Contrasting

Order By: Relevance

“…We have investigated quantum control of three fullynoisy channels in the context of quantum Shannon theory with superpositions of trajectories in the specific case of superposition of causal orders [7,13].…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Note that in the setup of Fig. 1, just as in the depolarising quantum switch, the subspace on which each channel acts is, technically, a nontrivial d-dimensional "sector" of he 2ddimensional joint control-target Hilbert space 4 [44], and so the channels cannot be strictly said to act trivially on the control system [32]. Indeed, in both cases the global channel acts to delocalise some of the information about the target into the correlations between the two systems.…”

Section: Communication Through Coherentlycontrolled Depolarising Chanmentioning

confidence: 99%

“…This is conceptually similar to the effect of quantum phase kickback associated with controlled unitary operations [1,45], and its role in such communication advantages is further explored in Refs. [40,41,44].…”

Section: Communication Through Coherentlycontrolled Depolarising Chanmentioning

confidence: 99%

“…We note, however, that Ref. [44] has recently introduced the notion of "vacuum-extended channels" as an alternative approach to capturing the implementation-dependence relevant to the coherent control of quantum channels. There, coherent control can be expressed as a supermap of the vacuum-extended channels corresponding to a particular implementation, allowing one to formally prove the absence of indefinite causal order (i.e., in that case, the causal separability) of the coherent control of such channels.…”

Section: Dependence On Channel Implementationmentioning

confidence: 99%

See 1 more Smart Citation

Communication through coherent control of quantum channels

Abbott

Wechs

Horsman

et al. 2020

Quantum

118

View full text Add to dashboard Cite

A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter\cite{ebler18}, it was however shown that if a quantum state passes through two such channels in a quantum superposition of different orders---a setup known as the ``quantum switch''---then information can nevertheless be transmitted through the channels. Here, we show that a similar effect can be obtained when one coherently controls between sending a target system through one of two identical depolarising channels. Whereas it is tempting to attribute this effect in the quantum switch to the indefinite causal order between the channels, causal indefiniteness plays no role in this new scenario. This raises questions about its role in the corresponding effect in the quantum switch. We study this new scenario in detail and we see that, when quantum channels are controlled coherently, information about their specific implementation is accessible in the output state of the joint control-target system. This allows two different implementations of what is usually considered to be the same channel to therefore be differentiated. More generally, we find that to completely describe the action of a coherently controlled quantum channel, one needs to specify not only a description of the channel (e.g., in terms of Kraus operators), but an additional ``transformation matrix'' depending on its implementation.

show abstract

“…Heuristically, this can be pictured as putting the order between A and B in a quantum superposition. More precisely, several approaches to indefinite causal orders have been proposed using 'process matrix' or 'quantum switch' [1][2][3][4][5][6]. In a recent article, Ebler et al argue that quantum control on causal order is a non-trivial resource that provides a non-classical communication advantage, i.e., two noisy channels in a quantum switch can transmit more information than any of these channels individually [7].…”

Section: Introductionmentioning

confidence: 99%

Channel capacity enhancement with indefinite causal order

Loizeau

Grinbaum

2020

Phys. Rev. A

View full text Add to dashboard Cite

Classical communication capacity of a channel can be enhanced either through a device called a 'quantum switch' or by putting the channel in a quantum superposition. The gains in the two cases, although different, have their origin in the use of a quantum resource, but is it the same resource? Here this question is explored through simulating large sets of random channels. We find that quantum superposition always provides an advantage, while the quantum switch does not: it can either increase or decrease communication capacity. The origin of this discrepancy can be attributed to a subtle combination of superposition and non-commutativity.

show abstract

Quantum Shannon theory with superpositions of trajectories

Cited by 114 publications

References 52 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

Communication through coherent control of quantum channels

Channel capacity enhancement with indefinite causal order

Contact Info

Product

Resources

About