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arXiv:2006.08190 · Physical Review Research

Engineering two-qubit mixed states with weak measurements

Parveen Kumar, Kyrylo Snizhko, Yuval Gefen

Published Oct 19, 2020• 17 citations
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Abstract

It is known that protocols based on weak measurements can be used to steer quantum systems into predesignated pure states.Here we show that weak-measurement-based steering protocols can be harnessed for on-demand engineering of mixed states.In particular, through a continuous variation of the protocol parameters, one can guide a classical target state to a discorded one, and further on, toward an entangled target state.

DOI
10.1103/physrevresearch.2.042014

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It is known that protocols based on weak measurements can be used to steer quantum systems into predesignated pure states.Here we show that weak-measurement-based steering protocols can be harnessed for on-demand engineering of mixed states.In particular, through a continuous variation of the protocol parameters, one can guide a classical target state to a discorded one, and further on, toward an entangled target state.
We set out a general protocol for steering the state of a quantum system from an arbitrary initial state toward a chosen target state by coupling it to auxiliary quantum degrees of freedom.The protocol requires multiple repetitions of an elementary step: During each step, the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term "detector qubits") that have been prepared in a specified initial state.The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes.The steering harnesses backaction of the detector qubits on the system, arising from entanglement generated during the coupled evolution.We establish principles for the design of the system-detector coupling that ensure steering of a desired form.We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state).We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering.Our protocols are amenable to implementations using present-day technology.Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.
We propose active steering protocols for quantum state preparation in quantum circuits where each system qubit is connected to a single detector qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost-function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on detector qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the NNN-qubit W state.
We set out a general protocol for steering the state of a quantum system from an arbitrary initial state towards a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: during each step the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term 'detector qubits') that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses back-action of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.
We propose active steering protocols for quantum state preparation in quantum circuits where each system qubit is connected to a single detector qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost-function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on detector qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the N -qubit W state. Published by the American Physical Society 2024
We introduce and analyze an active steering protocol designed to target multipartite entangled states. The protocol involves multiple qubits subjected to weak Bell pair measurements with active feedback, where the feedback operations are optimized to maximize the Quantum Fisher Information. Our scheme efficiently reaches a genuinely entangled one-parameter state manifold. Numerical simulations for systems with up to 22 qubits suggest that the protocol is scalable and allows high multipartite entanglement across the system.
The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak blind measurements (where the detector's readouts are traced out). Here we analyze the steering of a two-level system using the interplay of a system Hamiltonian and weak measurements and show that any pure or mixed state can be targeted. We show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high-purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, whereas for low-purity target states, it implies an oscillatory approach to the target state. The dynamical phase transition between these two regimes is characterized by a third-order exceptional point.