Noisy quantum metrology with the assistance of indefinite causal order

Abstract

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 probe-control 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 with ill-configured input probes, or in blind situations when the axis of the unitary is unknown. 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 gets inoperative. Measurement of the probe qubit of the switched channel is also shown to add useful capabilities for phase estimation. The results contribute to the analysis of switched quantum channels with indefinite order for information processing, and uncover new possibilities for qubit metrology.

29 pages, 7 figures, 52 references

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Cited by in corpus (23)

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• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Quantum parameter estimation on coherently superposed noisy channels
• Indefinite causal order for quantum metrology with quantum thermal noise
• Evading noise in multiparameter quantum metrology with indefinite causal order
• Fully-Optimized Quantum Metrology: Framework, Tools, and Applications
• Reassessing thermodynamic advantage from indefinite causal order
• Reassessing the advantage of indefinite causal orders for quantum metrology
• Experimentally demonstrating indefinite causal order algorithms to solve the generalized Deutsch's problem
• Breaking the limits of purification: Postselection enhances heat-bath algorithmic cooling
• Memory in quantum processes with indefinite time direction and causal order
• Quantum networks boosted by entanglement with a control system
• Activation of thermal states by coherently controlled thermalization processes
• Practical computational advantage from the quantum switch on a generalized family of promise problems
• Enhancing precision of atomic clocks by tuning disorder in accessories
• Indefinite causal order for quantum phase estimation with Pauli noise
• Indefinite Time Directed Quantum Metrology
• Quantum switch as a thermodynamic resource in the context of passive states
• Optimal quantum precision in noise estimation: Is entanglement necessary?
• Sequential device-independent certification of indefinite causal order
• Optimal Thermalization under Indefinite Causal Order with Identical and Asymmetric Baths
• Entropic uncertainty under indefinite causal order and input-output direction