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1. Precision Bounds on Continuous-Variable State Tomography Using Classical Shadows

   https://doi.org/10.1103/PRXQuantum.5.010346  

   Gandhari, Srilekha; Albert, Victor V.; Gerrits, Thomas; Taylor, Jacob M.; Gullans, Michael J. (March 2024, PRX Quantum 5)

   Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called “classical shadows,” with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon-number-resolving, and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with high probability, we show that homodyne detection requires order O(N4+1/3) measurements in the worst case, whereas photon-number-resolving and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental analyses of homodyne tomography match closely with our theoretical predictions. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements. 

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2. Homodyne measurement with a Schrödinger cat state as a local oscillator

   https://doi.org/10.48550/arXiv.2207.10210  

   Combes, Joshua; Lund, Austin (July 2022, ArXivorg)

   Homodyne measurements are a widely used quantum measurement. Using a coherent state of large amplitude as the local oscillator, it can be shown that the quantum homodyne measurement limits to a field quadrature measurement. In this work, we give an example of a general idea: injecting non-classical states as a local oscillator can led to non-classical measurements. Specifically, we consider injecting a superposition of coherent states, a Schrödinger cat state, as a local oscillator. We derive the Kraus operators and the positive operator-valued measure (POVM) in this situation and show the POVM is a reflection symmetric quadrature measurement when the coherent state amplitudes are large. 

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3. Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit

   https://doi.org/10.22331/q-2024-09-25-1480  

   Rodríguez-García, M A; Becerra, F E (September 2024, Quantum)

   Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0,\pi /2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0,\pi )$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology. 

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4. Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

   https://doi.org/10.22331/q-2022-02-02-638  

   Sierant, Piotr; Chiriacò, Giuliano; Surace, Federica M.; Sharma, Shraddha; Turkeshi, Xhek; Dalmonte, Marcello; Fazio, Rosario; Pagano, Guido (February 2022, Quantum)

   Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms. 

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5. Quantum back-action limits in dispersively measured Bose-Einstein condensates

   https://doi.org/10.1038/s42005-023-01181-5  

   Altuntaş, Emine; Spielman, I. B. (December 2023, Communications Physics)

   Abstract A fundamental tenet of quantum mechanics is that measurements change a system’s wavefunction to that most consistent with the measurement outcome, even if no observer is present. Weak measurements produce only limited information about the system, and as a result only minimally change the system’s state. Here, we theoretically and experimentally characterize quantum back-action in atomic Bose-Einstein condensates interacting with a far-from resonant laser beam. We theoretically describe this process using a quantum trajectories approach where the environment measures the scattered light and present a measurement model based on an ideal photodetection mechanism. We experimentally quantify the resulting wavefunction change in terms of the contrast of a Ramsey interferometer and control parasitic effects associated with the measurement process. The observed back-action is in good agreement with our measurement model; this result is a necessary precursor for achieving true quantum back-action limited measurements of quantum gases. 

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