Channel capacity enhancement with indefinite causal order

Loizeau, Nicolas; Grinbaum, Alexei

doi:10.1103/physreva.101.012340

Cited by 43 publications

(59 citation statements)

References 28 publications

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“…In a recent study [51] related to [8], a comparable effect is observed with no indefinite causal order, but instead with a coherent control to determine which of the two depolarizing channels is traversed. These are two distinct phenomena, which can be observed separately as in [8] and in [51], and which are further discussed in [52,11]. The effects for estimation in our study occur in the presence of coherent control of indefinite causal order, as in [8].…”

Section: Discussionmentioning

confidence: 56%

Noisy quantum metrology with the assistance of indefinite causal order

Chapeau‐Blondeau

2021

Phys. Rev. A

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A generic qubit unitary operator affected by depolarizing noise is duplicated and inserted in a quantum switch process realizing a superposition of causal orders. The characterization of the resulting switched quantum channel is worked out for its action on the joint state of the probecontrol qubit pair. The switched channel is then specifically investigated for the important metrological task of phase estimation on the noisy unitary operator, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional techniques of estimation where the noisy unitary is directly probed in a one-stage or two-stage cascade with definite order, or several uses of them with two or more qubits. In the switched channel with indefinite order, specific properties are reported, meaningful for estimation and not present with conventional techniques. It is shown that the control qubit, although it never directly interacts with the unitary, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. Also, measurement of the control qubit maintains the possibility of efficient estimation in difficult conditions where conventional estimation becomes less efficient, as for instance with ill-configured input probes, or in blind situations when the axis of the unitary is unknown. Especially, effective estimation by measuring the control qubit remains possible even when the input probe tends to align with the axis of the unitary, or with a fully depolarized input probe, while in these conditions conventional estimation becomes inoperative. Measurement of the probe qubit of the switched channel is also analyzed and shown to add useful capabilities for phase estimation. The results contribute to the ongoing identification and analysis of the properties and capabilities of switched quantum channels with indefinite order for information processing, and uncover new possibilities for quantum estimation and qubit metrology.

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Section: Discussionmentioning

confidence: 56%

Noisy quantum metrology with the assistance of indefinite causal order

Chapeau‐Blondeau

2021

Phys. Rev. A

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“…Nevertheless, a related recent result has also shown that, for certain choices of noisy channels, the quantum switch can enable perfect quantum communication, but that this impossible with our setup [52]. Understanding when the quantum switch or the coherent control of channels is a more powerful communication resource [39], as well as the role of indefinite causal order in communication advantages provided by the quantum switch [41], are crucial questions that remain the be fully answered.…”

Section: Discussionmentioning

confidence: 93%

“…Thus, one may intuitively expect the target system to be less "degraded" in the scenario considered here. However, a recent paper exploring numerically this issue [39] (which appeared subsequent to an earlier preprint of this manuscript and, in part, in response to the very questions we raise) indicates that the situation is more subtle, with the noncommutativity of the Kraus operators of the two channels placed inside a quantum switch also playing a role in these communication advantages. In particular, in some cases the quantum switch indeed outperforms coherent control meaning this intuition-at least applied naively-is incorrect, although further study is needed to understand fully the situation.…”

Section: A3 Examplesmentioning

confidence: 93%

“…Nevertheless, the fact that coherent control-of channel or of order-plays a role in transmitting information through fully depolarising channels in both these scenarios raises questions about the role of indefinite causal order in the result of Ref. [3] using the quantum switch, or, at least, the relative role of causal indefiniteness and coherent control [39]. Similar questions, as well as the need to clarify how to compare different such advantages, have also been raised recently based on different considerations in Ref.…”

Section: Communication Through Coherentlycontrolled Depolarising Chanmentioning

confidence: 99%

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Communication through coherent control of quantum channels

Abbott

Wechs

Horsman

et al. 2020

Quantum

118

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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.

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“…A typical and striking benefit is when the two channels (1) and ( 2) are two completely depolarizing quantum channels, which are therefore individually incapable of transmitting any useful information. It has then been shown that when two such channels are associated into a switched channel with indefinite order [3,7], or into a coherently superposed channel [4,7], in each scheme effective information communication becomes possible. Comparison has been performed and discussed [4,7,8] to better appreciate the mechanisms and specificities of the two schemes, and the respective roles of indefinite order and of coherent superposition, particularly in reaching similar capabilities of information communication through depolarizing channels.…”

Section: Introductionmentioning

confidence: 99%

Quantum parameter estimation on coherently superposed noisy channels

Chapeau‐Blondeau

2021

Phys. Rev. A

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A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A characterization is performed of the transformation realized by the superposed channel on the joint state of the probe-control qubit pair. The superposed channel is then specifically analyzed for the fundamental metrological task of phase estimation on the noisy unitary, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional estimation techniques and also with a quantum switched channel with indefinite causal order recently investigated for a similar task of phase estimation. In the analysis here, a first important observation is that the control qubit of the superposed channel, although it never directly interacts with the unitary being estimated, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. This property is also present with the switched channel but is inaccessible with conventional techniques. The optimal measurement of the control qubit here is characterized in general conditions. A second important observation is that the noise plays an essential role in coupling the control qubit to the unitary, and that the control qubit remains operative for phase estimation at very strong noise, even with a fully depolarizing noise, whereas conventional estimation and the switched channel become inoperative in these conditions. The results extend the analysis of the capabilities of coherently controlled channels which represent novel devices exploitable for quantum signal and information processing.

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Channel capacity enhancement with indefinite causal order

Cited by 43 publications

References 28 publications

Noisy quantum metrology with the assistance of indefinite causal order

Noisy quantum metrology with the assistance of indefinite causal order

Communication through coherent control of quantum channels

Quantum parameter estimation on coherently superposed noisy channels

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