The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that projective measurements can be constructed from sequential generalized or weak measurements, there is still lack of a proof of this hypothesis in general cases. Here we prove it from the perspective of quantum channels. We show that projective measurements naturally arise from sequential generalized measurements in the asymptotic limit, when the measurement operators are normal and commuting with each other. Specifically, a selective projective measurement arises from a set of typical sequences of selective generalized measurements. We also provide an explicit scheme to construct projective measurements of a quantum system with sequential generalized measurements. Remarkably, a single ancilla qubit is sufficient to mediate sequential generalized measurements for constructing arbitrary projective measurements of a generic system, which can have applications in readout, initialization, and feedback control of a quantum system. As an example, we present a protocol to measure the modular excitation numbers of a bosonic mode with an ancilla qubit.The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that projective measurements can be constructed from sequential generalized or weak measurements, there is still lack of a proof of this hypothesis in general cases. Here we prove it from the perspective of quantum channels. We show that projective measurements naturally arise from sequential generalized measurements in the asymptotic limit, when the measurement operators are normal and commuting with each other. Specifically, a selective projective measurement arises from a set of typical sequences of selective generalized measurements. We also provide an explicit scheme to construct projective measurements of a quantum system with sequential generalized measurements. Remarkably, a single ancilla qubit is sufficient to mediate sequential generalized measurements for constructing arbitrary projective measurements of a generic system, which can have applications in readout, initialization, and feedback control of a quantum system. As an example, we present a protocol to measure the modular excitation numbers of a bosonic mode with an ancilla qubit.

arXiv:2208.08141Physical Review AJan 25, 20239 citations

Quantum Measurement

Biao Wu

Springer eBooksJan 1, 20230 citations

Generalized measurements on qubits in quantum randomness certification and expansion

Piotr Mironowicz, Marcus Grünfeld, Mohamed Bourennane

Quantum mechanics has greatly impacted our understanding of microscopic nature. One of the key concepts of this theory is generalized measurements, which have proven useful in various quantum information processing tasks. However, despite their significance, they have not yet been shown empirically to provide an advantage in quantum randomness certification and expansion protocols. This investigation explores scenarios where generalized measurements can yield more than 1 bit of certified randomness with a single-qubit system measurement on untrusted devices and against a quantum adversary. We compare the robustness of several protocols to exhibit the advantage of exploiting generalized measurements. In our analysis of experimental data, we were able to obtain 1.21 bits of min-entropy from a measurement taken on one qubit of an entangled state. We also obtained 1.07 bits of min-entropy from an experiment with quantum state preparation and generalized measurement on a single qubit. We also provide finite data analysis for a protocol using generalized measurements and the Entropy Accumulation Theorem. Our exploration demonstrates the potential of generalized measurements to improve the certification of quantum sources of randomness and enhance the security of quantum cryptographic protocols and other areas of quantum information. Published by the American Physical Society 2024Quantum mechanics has greatly impacted our understanding of microscopic nature. One of the key concepts of this theory is generalized measurements, which have proven useful in various quantum information processing tasks. However, despite their significance, they have not yet been shown empirically to provide an advantage in quantum randomness certification and expansion protocols. This investigation explores scenarios where generalized measurements can yield more than 1 bit of certified randomness with a single-qubit system measurement on untrusted devices and against a quantum adversary. We compare the robustness of several protocols to exhibit the advantage of exploiting generalized measurements. In our analysis of experimental data, we were able to obtain 1.21 bits of min-entropy from a measurement taken on one qubit of an entangled state. We also obtained 1.07 bits of min-entropy from an experiment with quantum state preparation and generalized measurement on a single qubit. We also provide finite data analysis for a protocol using generalized measurements and the Entropy Accumulation Theorem. Our exploration demonstrates the potential of generalized measurements to improve the certification of quantum sources of randomness and enhance the security of quantum cryptographic protocols and other areas of quantum information. Published by the American Physical Society 2024

arXiv:2410.11082Physical Review AppliedOct 17, 20245 citations

Why measurements are made of effects

Tobias Fritz

Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$ -tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.

quant-pharXiv:2602.18898Feb 24, 20260 citations

Both in quantum theory and in general probabilistic theories, measurements with

n

outcomes are modelled as

n

-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.