We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated with precision scaling as 1/T , where T is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum Master equation, implying at most 1/ √ T scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction like protocol must satisfy in order to regain the 1/T precision scaling in case the above mentioned algebraic condition is not satisfied. Furthermore, we apply the developed methods to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of non-linear metrological models.
We establish general limits on how precise a parameter, e.g., frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (∼ 1/N 2 ) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (∼ 1/N ) even when allowing for the full power of fast control. The latter holds both in the single-shot and infinitelymany repetitions scenarios. However, even in this case allowing for fast quantum control helps to improve the asymptotic constant factor. Furthermore, for frequency estimation with finite resource we show how a parallel scheme utilizing any fixed number of entangled qubits but no fast quantum control can be outperformed by a simple, easily implementable, sequential scheme which only requires entanglement between one sensing and one auxiliary qubit.
Quantum theory is often presented as the theory describing the microscopic world, and admittedly, it has done this extremely well for decades. Nonetheless, the question of whether it applies to macroscopic scales remains open, despite many efforts1, 2, 3. Here, we report on entanglement exhibiting strong analogies with the Schrödinger cat state as it involves two macroscopically distinct states- two states that can be efficiently distinguished using detectors with no microscopic resolution4. Specifically, we start by generating entanglement between two spatial optical modes at the single-photon level and subsequently displace one of these modes up to almost a thousand photons5. To reliably check whether entanglement is preserved, the state is redisplaced back to the single-photon level and a well-established entanglement measure6, based on single-photon detection, is applied. Our results provide a tool to address fundamental questions about quantum theory and hold potential for more applied problems, for instance in quantum sensing
Large-scale quantum effects have always played an important role in the foundations of quantum theory. With recent experimental progress and the aspiration for quantum enhanced applications, the interest in macroscopic quantum effects has been reinforced. In this review, we critically analyze and discuss measures aiming to quantify various aspects of macroscopic quantumness. We survey recent results on the difficulties and prospects to create, maintain and detect macroscopic quantum states. The role of macroscopic quantum states in foundational questions as well as practical applications is outlined. Finally, we present past and on-going experimental advances aiming to generate and observe macroscopic quantum states.
We propose an experimentally accessible scheme to determine the lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the measurement statistics of a state before and after a small unitary rotation. We argue that, in general, the limited resolution of collective observables prevents the detection of large QFI. This can be overcome by performing an additional operation prior to the measurement. We illustrate the power of this protocol for present-day spin-squeezing experiments, where the same operation used for the preparation of the initial spin-squeezed state improves also the measurement precision and hence the lower bound on the QFI by 2 orders of magnitude. We also establish a connection to the Leggett-Garg inequalities. We show how to simulate a variant of the inequalities with our protocol and demonstrate that large QFI is necessary for their violation with coarse-grained detectors.
We show theoretically that a large Bell inequality violation can be obtained with human eyes as detectors, in a ''micro-macro'' experiment where one photon from an entangled pair is greatly amplified via stimulated emission. The violation is robust under photon loss. This leads to an apparent paradox, which we resolve by noting that the violation proves the existence of entanglement before the amplification. The same is true for the micro-macro experiments performed so far with conventional detectors. However, we also prove that there is genuine micro-macro entanglement even for high loss.
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