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1. Time-Energy Uncertainty Relation for Noisy Quantum Metrology

   https://doi.org/10.1103/PRXQuantum.4.040336  

   Faist, Philippe ; Woods, Mischa P. ; Albert, Victor V. ; Renes, Joseph M. ; Eisert, Jens ; Preskill, John ( December 2023 , PRX Quantum)

   Detection of very weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. To sense an unknown physical parameter, one prepares an initial state of a probe system, allows the probe to evolve as governed by a Hamiltonian H for some time t, and then measures the probe. If H is known, we can estimate t by this method; if t is known, we can estimate classical parameters on which H depends. The accuracy of a quantum sensor can be limited by either intrinsic quantum noise or by noise arising from the interactions of the probe with its environment. In this work, we introduce and study a fundamental trade-off, which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which a party Alice prepares an initial pure state of the clock, allows the clock to evolve for a time that is not precisely known, and then transmits the clock through a noisy channel to a party Bob. Meanwhile, the environment (Eve) receives any information about the clock that is lost during transmission. We prove that Bob’s loss of quantum Fisher information about the elapsed time is equal to Eve’s gain of quantum Fisher information about a complementary energy parameter. We also prove a similar, but more general, trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two noncommuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise, which form a subset of the Knill-Laflamme error-correction conditions. A state and its local time-evolution direction, if they satisfy these conditions, are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of the trade-off relation to sensing using a quantum many-body probe subject to erasure or amplitude-damping noise. 

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2. Integrated quantum optical phase sensor in thin film lithium niobate

   https://doi.org/10.1038/s41467-023-38246-6  

   Stokowski, Hubert S. ; McKenna, Timothy P. ; Park, Taewon ; Hwang, Alexander Y. ; Dean, Devin J. ; Celik, Oguz Tolga ; Ansari, Vahid ; Fejer, Martin M. ; Safavi-Naeini, Amir H. ( June 2023 , Nature Communications)

   The quantum noise of light, attributed to the random arrival time of photons from a coherent light source, fundamentally limits optical phase sensors. An engineered source of squeezed states suppresses this noise and allows phase detection sensitivity beyond the quantum noise limit (QNL). We need ways to use quantum light within deployable quantum sensors. Here we present a photonic integrated circuit in thin-film lithium niobate that meets these requirements. We use the second-order nonlinearity to produce a squeezed state at the same frequency as the pump light and realize circuit control and sensing with electro-optics. Using 26.2 milliwatts of optical power, we measure (2.7 ± 0.2)% squeezing and apply it to increase the signal-to-noise ratio of phase measurement. We anticipate that photonic systems like this, which operate with low power and integrate all of the needed functionality on a single die, will open new opportunities for quantum optical sensing.

    

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3. Loss-tolerant all-optical distributed sensing

   https://doi.org/10.1364/CLEO_AT.2024.ATh1G.6  

   Nehra, Rajveer ; Oh, Changhun ; Jiang, Liang ; Marandi, Alireza ( January 2024 , Optica Publishing Group)

   We investigate a resource-efficient distributed quantum sensing (DQS) scheme using phase-sensitive optical parametric amplifiers and linear optics, achieving sensitivity levels close to the optimal limit determined by the quantum Fisher information of the resource state.

    

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4. Time-reversal-based quantum metrology with many-body entangled states

   https://doi.org/10.1038/s41567-022-01653-5  

   Colombo, Simone ; Pedrozo-Peñafiel, Edwin ; Adiyatullin, Albert F. ; Li, Zeyang ; Mendez, Enrique ; Shu, Chi ; Vuletić, Vladan ( July 2022 , Nature Physics)

   Linear quantum measurements with independent particles are bounded by the standard quantum limit, which limits the precision achievable in estimating unknown phase parameters. The standard quantum limit can be overcome by entangling the particles, but the sensitivity is often limited by the final state readout, especially for complex entangled many-body states with non-Gaussian probability distributions. Here, by implementing an effective time-reversal protocol in an optically engineered many-body spin Hamiltonian, we demonstrate a quantum measurement with non-Gaussian states with performance beyond the limit of the readout scheme. This signal amplification through a time-reversed interaction achieves the greatest phase sensitivity improvement beyond the standard quantum limit demonstrated to date in any full Ramsey interferometer. These results open the field of robust time-reversal-based measurement protocols offering precision not too far from the Heisenberg limit. Potential applications include quantum sensors that operate at finite bandwidth, and the principle we demonstrate may also advance areas such as quantum engineering, quantum measurements and the search for new physics using optical-transition atomic clocks. 

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5. Enhancing the sensitivity of an atom interferometer to the Heisenberg limit using increased quantum noise

   https://doi.org/10.1364/JOSAB.396358  

   Fang, Renpeng ; Sarkar, Resham ; Shahriar, Selim_M ( June 2020 , Journal of the Optical Society of America B)

   In a conventional atomic interferometer employing$N$atoms, the phase sensitivity is at the standard quantum limit:$1/\sqrt{N}$. Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of$1/N$, while increasing the quantum noise by$\sqrt{N}$and amplifying the phase by a factor of$N$. Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of$N$atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is$N$when$N$is even, and is vanishingly small when$N$is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of$N$. Thus, for a situation where the probability of$N$being even or odd is equal, the net sensitivity is within a factor of$\sqrt{2}$of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.

    

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