Quantum Circuits with Classical Versus Quantum Control of Causal Order

Wechs, Julian; Dourdent, Hippolyte; Abbott, Alastair A.; Branciard, Cyril

doi:10.1103/prxquantum.2.030335

Cited by 43 publications

(49 citation statements)

References 63 publications

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“…Note that there are also unitary processes with two input operations-i.e., variations of the quantum switch-that have realisations of the kind considered here (for instance, one obtains such a realisation when one fixes Alice's or Bob's operation in the circuit 7). This raises the question of whether, conversely, the process considered in this work could have an alternative, more intuitive interpretation as a "superposition" of processes with different definite causal orders in some sense (although it cannot be achieved by direct multipartite generalisations of the quantum switch [27]). The decomposition of this process into a direct sum of causal unitary processes shown in [31] may offer insights into this question.…”

Section: Discussionmentioning

confidence: 99%

“…We have shown that certain quantum processes with indefinite causal order, namely unitary extensions of tripartite processes, have realisations on time-delocalised subsystems. This class contains particularly interesting examples that cannot be understood as arising from quantum control of the order of operations [27], and that violate causal inequalities. We considered a well-known example of a classical, deterministic noncausal process, and studied explicitly its realisation on time-delocalised subsystems-or, in this case, time-delocalised classical variables.…”

Section: Discussionmentioning

confidence: 99%

“…where |U X ∈ H X IO X IO are the pure Choi representations of the local unitary operations U X , and " * " denotes here the so-called vector link product [27] (cf. Appendix A).…”

Section: The Process Matrix Frameworkmentioning

confidence: 99%

“…Consider two tensor product Hilbert spaces H XY = H X ⊗H Y and H Y Z = H Y ⊗ H Z which share the same (possibly trivial) space factor H Y , and with non-overlapping H X , H Z . The link product of any two vectors |a ∈ H XY and |b ∈ H Y Z is defined (with respect to the computational basis {|i Y } i of H Y ) as [27] |a * |b…”

Section: Construction Of the Temporal Circuitmentioning

confidence: 99%

“…that takes the target, control and ancillary systems to the input Hilbert space of the "global future" party and the system H f , which is then traced out (which does however not introduce any decoherence, since f always ends up in the state |0 f , when p is prepared in the state |0 p ). Such a circuit is an example of a quantum circuit with quantum control of causal order [27], and similarly to the case of fixed-order quantum circuits, the operations ω 1 , ω • 2 , ω • 2 and ω 3 can be constructed explicitly from the process matrix.…”

mentioning

confidence: 99%

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Existence of processes violating causal inequalities on time-delocalised subsystems

Wechs¹,

Branciard²,

Oreshkov³

2022

Preprint

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It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how such processes can be realised in practice. In order to provide a rigorous argument for the notion that certain such processes have a realisation in standard quantum theory, the concept of time-delocalised quantum subsystem has been introduced. In this paper, we show that realisations on time-delocalised subsystems exist for all unitary extensions of tripartite processes. Remarkably, this class contains processes that violate causal inequalities, i.e., that can generate correlations that witness the incompatibility with definite causal order in a device-independent manner. We consider a known striking example of such a tripartite classical process that has a unitary extension, and study its realisation on time-delocalised subsystems. We then discuss the question of what a violation of causal inequalities implies in this setting, and argue that it is indeed a meaningful concept to show the absence of a definite causal order between the variables of interest.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…where |U X ∈ H X IO X IO are the pure Choi representations of the local unitary operations U X , and " * " denotes here the so-called vector link product [27] (cf. Appendix A).…”

Section: The Process Matrix Frameworkmentioning

confidence: 99%

Section: Construction Of the Temporal Circuitmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Existence of processes violating causal inequalities on time-delocalised subsystems

Wechs¹,

Branciard²,

Oreshkov³

2022

Preprint

Self Cite

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show abstract

Semantics of quantum programming languages: Classical control, quantum control

Valiron

2022

Journal of Logical and Algebraic Methods in Programming

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Existence of processes violating causal inequalities on time-delocalised subsystems

Wechs

Branciard

Oreshkov³

2023

Nat Commun

Self Cite

View full text Add to dashboard Cite

It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how such processes can be realised in practice. In order to provide a rigorous framework for the notion that certain such processes have a realisation in standard quantum theory, the concept of time-delocalised quantum subsystem has been introduced. In this paper, we show that realisations on time-delocalised subsystems exist for all unitary extensions of tripartite processes. This class contains processes that violate causal inequalities, i.e., that can generate correlations that witness the incompatibility with definite causal order in a device-independent manner, and whose realisability has been a central open problem. We consider a known example of such a tripartite classical process that has a unitary extension, and study its realisation on time-delocalised subsystems. We then discuss this finding with regard to the assumptions that underlie causal inequalities, and argue that they are indeed a meaningful concept to show the absence of a definite causal order between the variables of interest.

show abstract

Quantum Circuits with Classical Versus Quantum Control of Causal Order

Cited by 43 publications

References 63 publications

Existence of processes violating causal inequalities on time-delocalised subsystems

Existence of processes violating causal inequalities on time-delocalised subsystems

Semantics of quantum programming languages: Classical control, quantum control

Existence of processes violating causal inequalities on time-delocalised subsystems

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