Multifold behavior of the information transmission by the quantum 3-switch

Procopio, Lorenzo M.; Delgado, Francisco; Enríquez, Marco; Belabas, Nadia

doi:10.1007/s11128-021-03159-0

Cited by 2 publications

(4 citation statements)

References 28 publications

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“…However, in Ref. [20], it was found that the transmission of classical information with three channels in superposition of causal orders has a threefold behaviour. These behaviours are based on the properties of three equivalent classes of quantum switch matrices ρ (m) out (θ).…”

Section: Quantum Fisher Informationmentioning

confidence: 99%

“…where the subscript 8 stands for the label of the quantum 3-switch matrix associated to a specific combination of causal order, see [20]. By introducing the output state (20) and the score operator ( 21) into ( 9), we found that the block matrix elements from (21) are…”

Section: Quantum Fisher Information For M Causal Ordersmentioning

confidence: 99%

“…where the subscript 8 stands for the label of the quantum 3-switch matrix associated to a specific combination of causal order, see [20]. For m = 4 causal orders, the complete expression for the quantum Fisher information (29) is…”

Section: Appendix B Analytical Expressions Of the Quantum Fisher Info...mentioning

confidence: 99%

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Parameter Estimation via Indefinite Causal Structures

Procopio

2023

J. Phys.: Conf. Ser.

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Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three noisy channels for the case where the channels are in superposition of causal orders. We found that the quantum Fisher information increases as the number of causal orders increases for certain combinations. We also show that certain combinations of causal orders attain higher precision on bounds than others for the same number of causal orders. Based on our results, we chose the best combinations of causal orders with three channels for probing schemes using indefinite causal structures.

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Section: Quantum Fisher Informationmentioning

confidence: 99%

Section: Quantum Fisher Information For M Causal Ordersmentioning

confidence: 99%

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Parameter Estimation via Indefinite Causal Structures

Procopio

2023

J. Phys.: Conf. Ser.

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“…1). It has become an interesting resource with applications in quantum computing [11][12][13][14][15], quantum communication complexity [16][17][18], communication through noisy channels [19][20][21][22][23][24][25][26][27][28], quantum thermodynam-Figure 1: The simplest quantum switch applies two gates in two different orders, which is coherently controlled by a control qubit. In photonic realizations, the order of the operations can be controlled by the path degree of freedom of photons, which we illustrate by colour wires.…”

Section: Introductionmentioning

confidence: 99%

Practical computational advantage from the quantum switch on a generalized family of promise problems

Jorge

Delgado

Walborn

2023

Quantum

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The quantum switch is a quantum computational primitive that provides computational advantage by applying operations in a superposition of orders. In particular, it can reduce the number of gate queries required for solving promise problems where the goal is to discriminate between a set of properties of a given set of unitary gates. In this work, we use Complex Hadamard matrices to introduce more general promise problems, which reduce to the known Fourier and Hadamard promise problems as limiting cases. Our generalization loosens the restrictions on the size of the matrices, number of gates and dimension of the quantum systems, providing more parameters to explore. In addition, it leads to the conclusion that a continuous variable system is necessary to implement the most general promise problem. In the finite dimensional case, the family of matrices is restricted to the so-called Butson-Hadamard type, and the complexity of the matrix enters as a constraint. We introduce the “query per gate'' parameter and use it to prove that the quantum switch provides computational advantage for both the continuous and discrete cases. Our results should inspire implementations of promise problems using the quantum switch where parameters and therefore experimental setups can be chosen much more freely.

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Multifold behavior of the information transmission by the quantum 3-switch

Cited by 2 publications

References 28 publications

Parameter Estimation via Indefinite Causal Structures

Parameter Estimation via Indefinite Causal Structures

Practical computational advantage from the quantum switch on a generalized family of promise problems

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