Postselected Measurement Research Articles

Orthogonality catastrophe beyond bosonization from post-selection

We show that the dynamics induced by post-selected measurements can serve as a controlled route to access physical processes beyond the boundaries of Luttinger liquid physics. We consider a one-dimensional fermionic wire whose dynamics results from a sequence of weak measurements of the fermionic density at a given site, interspersed with unitary hopping dynamics. This realizes a non-Hermitian variant of the celebrated instance of a local scatterer in a fermionic system and its ensuing orthogonality catastrophe. We observe a distinct crossover in the system's time evolution as a function of the fermion density. In the high-density regime, reminiscent of the Hermitian case, a bosonized version of the model properly describes the dynamics while, as we delve into the low-density regime, the validity of bosonization breaks down, giving rise to irreversible behavior. Notably, this crossover from reversible to irreversible dynamics is nonperturbative in the measurement rate and can manifest itself even with relatively shallow measurement rates, provided that the system's density remains below the crossover threshold. Our results render a conceptually transparent model for exploring nonperturbative effects beyond bosonization, which could be used as a stepping stone to explore novel routes for the control of nonlinear dynamics in low-dimensional quantum systems. Published by the American Physical Society 2024

Many-Body Dynamics in Monitored Atomic Gases without Postselection Barrier.

We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. The properties of the quantum trajectories describing the atomic cloud drastically depend on the monitoring protocol and are distinct from those of the average density matrix. By varying the strength of the external drive, a measurement-induced phase transition occurs separating two phases with entanglement entropy scaling subextensively with the system size. Incidentally, the critical point coincides with the superradiance transition of the trajectory-averaged dynamics. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the postselection measurement problem, even in the case of imperfect monitoring.

Quantum phase fluctuation of pointer state in a post-selected measurement system

Post-selected measurement is used as a fundamental axiom in quantum optics. Here, a standard model of post-selected measurement with the input coherent pointer state is considered and the influence of weak value parameters on the quantum phase distribution function is studied on the basis of some analytical calculations. On the other hand, the effects of post-selected measurement on quantum phase fluctuations of the input coherent pointer states have been investigated, where the Barnett-Pegg formalism for the measured phase operators is assumed. It has been observed that the quantum phase fluctuations depend on some parameters such as the coupling strength, average value of input photon number, phase angle of the input coherent pointer state and two fundamental parameters of the complex weak value. Lastly, the presence of nonclassical effect is also checked for different parameters of quantum phase fluctuations.

Optimizing the trade off between precision and probability in post-selection estimation of the coupling of trapped ion system

In post-selection quantum measurement, it is a dilemma to obtain both high precision and large post-selection probability. Here,we deeply examine quantum Fisher information and probability of post-selection quantum measurement based on the trapped ion system, where the internal electronic state of the trapped ion acts as an interested system and the external motional state as a pointer. Based on the bichromatic excitation of the trapped ion, in the Lamb-Dicke regime we observe the dynamical behaviors of quantum Fisher information of estimating coupling parameter and post-selection probability under the various phase difference of the bichromatic laser. We find that the oscillations of quantum Fisher information and post-selection probability can be simultaneously enhanced by selecting appropriately the phase difference of the bichromatic laser, the amplitude and the phase of the pointer state. Although the competition between quantum Fisher information and the post-selection probability still exists in the whole coupling range, a trade-off point in the moderate-coupling regime where the precision and the probability surpass their convergence values in the strong coupling regime can be obtained. It means that there is a possibility that the desired precision and post-selection probability can be simultaneously achieved.

NOON-state generation and superresolved interference in a double-slit experiment

Maximally entangled NOON states are proposed to be generated with $N$ independent photons and a fixed double-slit in the Young's interference experiment. A strict condition is required that these photons have to be arranged in a straight line and separated from each other by certain equal distances. The initial product state turns into a NOON state of the photons at the double-slit, after $N$-photon postselected measurements. With a spatially random laser beam, we experimentally investigate the high-order correlation functions to imitate the behavior of the single-photon and $N$-photon wave packets of the NOON states. Since the $N$-photon wave packet is the product of $N$ single-photon wave packets, two methods are adopted to observe the superresolved fringes. The first method is to use the product of the second-order correlation functions. The second one is to measure the $2N\mathrm{th}$-order correlation functions. In the both cases, the superresolved fringes of up to fourth order are successfully observed.

Single-photon-added coherent state-based measurement transition and its advantages in precision measurement

In this work, the measurement transition as well as precision measurement advantages of single-photon-added coherent state after postselected von Neumann measurement are investigated. We noticed that the weak-to-strong measurement transition characterized by the shifts of pointer’s position and momentum variables occurred in continuously by controlling a dimensionless parameter associated with system–pointer coupling. We calculate the ratio between the signal-to-noise ratios of non-postselected and postselected measurements, and the latter is used to find the quantum Fisher information. We found that the single-photon-added coherent pointer state can improve the precision of the measurement processes such as signal-to-noise ratio and parameter estimation after postselected von Neumann measurement characterized by postselection and weak value. Furthermore, contrary to the results of several previous studies, we found that the anomalous large weak values cannot improve the precision measurement processes related to single-photon-added coherent state.

Quantum dynamical resource theory under resource non-increasing framework

We define the resource non-increasing (RNI) framework to study the dynamical resource theory. With this definition, we propose several potential quantification candidates under various free operation sets. For explicit demonstrations, we quantify the quantum dynamical coherence in the scenarios with and without post-selective measurements. Correspondingly, we show that the maximally incoherent operations (MIO) and the incoherent operations (IO) in the static coherence resource theory are free in the sense of dynamical coherence. We also provide operational meanings for the measures by the quantum discrimination tasks. Moreover, for the dynamical total coherence, we also present convenient measures and give the analytic calculation for the amplitude damping channel.

Studying the squeezing effect and phase-space distribution of a single-photon-added coherent state using a postselected von Neumann measurement

In this paper, ordinary and amplitude-squared squeezing as well as Wigner functions of single-photon-added coherent state after postselected von Neumann measurements are investigated. The analytical results show that the weak measurement procedure, which is characterized by postselection and weak value, can significantly change the principal squeezing feature of the single-photon-added coherent state. From the analysis of the Winger function we notice that in the strong measurement regime significant interference structures manifest and the negative regions become larger than the initial pointer state. Our results indicate that after postselected von Neumann measurement the degree of nonclassicality of single-photon-added coherent state is increased. It is anticipated that this work may provide alternate and effective methods for solving the state optimization problems based on the single-photon-added coherent state pointer via a postselected von Neumann measurement technique.

Interferometric weak value of polarization observable and differential Jones matrix algebra

The quantification of simultaneously present weak polarization anisotropy effects are of practical interest from polarimetric and metrological perspective. Recently, in Modak et al (2021 Phys. Rev. A 103 053518), we experimentally demonstrated a classical analog of post-selected quantum weak measurement through optical interferometry to amplify all possible weak polarization anisotropy effects individually. Here, we propose an extension of this interferometric framework for applying it in a realistic scenario to quantify simultaneously present polarization anisotropy effects. Moreover, a clear correspondence of differential Jones matrix approach with the present scheme is indicated. The proposed scheme enables the measurement of differential Jones matrices through characteristic Stokes vector elements. Our proposal leads to a new class of polarimeter for experimental detection of differential Jones matrix of non-depolarizing anisotropic medium exhibiting simultaneous multiple polarimetric effects of tiny magnitude.

Amplitude-squared squeezing of Schrödinger cat states via postselected von Neumann measurement

We know that the original Schr\"odinger cat states has no amplitude-squared squeezing. In this paper, we investigate the amplitude-squared squeezing of Schr\"odinger cat states using postselected von Neumann measurement. The results show that after postselected von Neumann measurement, the amplitude-squared squeezing of Schr\"odinger cat states change dramatically and this can be considered a result of weak value amplification. The squeezing effect also investigated by studying the Wigner function of Schr\"odinger cat states after postselected measurement.

Quantum postselective measurements: Sufficient condition for overcoming the Holevo bound and the role of max-relative entropy

The operation of unambiguous state discrimination (USD) plays an important role in quantum information theory. Here, we study the generalization for this operation which can be applied where USD is not available, including the case of completely coinciding supports. We demonstrate the effect of overcoming the Holevo bound after postselective measurements, which works for a class of ensembles, including two arbitrary noncommuting quantum states. We also discuss the role of max-relative entropy in postselective measurements and give an alternative operational interpretation for this function.

Scalable multiphoton quantum metrology with neither pre- nor post-selected measurements

The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.

Implementation of weak measurement amplification with the weak coherent light and optomechanical system

Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.

Interference-based weak-value amplification effects in post-selected weak measurement

Weak measurement (WM) based on post-selection is a useful tool for precision metrology due to the ability of amplifying weak physical effects. In this paper, we reveal the underlying mechanism of the amplification in the post-selected WM based on the weak-value amplification (WVA) and the almost balanced weak-values amplification (ABWVA) strategies. We find that the amplification stems from the interference between the local oscillator and signal components which are respectively associated with the initial system state and the state disturbance induced by the weak coupling. The magnitude of the amplification is proportional to the interference strength which is dominated by the post-selection and the coupling strength. Furthermore, our theory can perfectly explain the amplification limit in the WVA strategy and the anomalous amplification in the ABWVA strategy.

Channels, measurements, and postselection in quantum thermodynamics.

We analyze the benefit, in terms of extracting work, of having a single use of a quantum channel or measurement in quantum thermodynamics. This highlights a connection between unital and catalytic channels, and some subtleties concerning the conditional work cost of implementing a measurement given that a certain result was obtained. We also consider postselected measurements and show that any nontrivial postselection leads to an unbounded work benefit.

Quantum gates by adiabatic and superadiabatic probabilistic controlled evolutions

Adiabatic and superadiabatic controlled evolutions are used as universal models for quantum computations, where an auxiliary system is used as the main resource in the theory. While the adiabatic case demands a slow dynamics (so that the adiabatic theorem is satisfied), the superadiabatic model can speed up such process by spending more energy than the adiabatic one. In this paper, we explore a hybrid scheme of controlled evolutions and measurement in order to optimize the thermodynamic cost of implementing quantum gates. By adjusting a free parameter of the theory of controlled evolutions, we show that we can improve the energy cost of the evolution. To this end, we used a model of computation based on adiabatic/superadiabatic evolution and post-selection measurement on the auxiliary qubit. In both cases, adiabatic and superadiabatic, the probabilistic model allows for optimizing the thermodynamics cost of implementing gates. When the system reservoir interaction is taken into account, we show that the superadiabatic probabilistic model is more robust than the adiabatic one.

648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).

Effects of postselected von Neumann measurement on nonclassicality of single-photon-added coherent state

The effects of von Neumann postselected measurement on nonclassicality of single-photon-added coherent state (SPACS) are studied. Explicit expressions and analytical results for various field properties of SPACS such as the photon number distribution, the Mandel Q_{m} factor and the squeezing parameter of field quadrature after postselected von Neumann measurement are investigated. The results showed that the nonclassicality of SPACS after measurement changed dramatically than initial state. The measurement let SPACS possess more strong sub-Poissonian photon statistics in some definite coupling strength regimes and large weak values which accompanied by low postselection probabilities.

Multiparameter quantum metrology with postselection measurements

We analyze simultaneous quantum estimations of multiple parameters with postselection measurements in terms of a trade-off relation. The system, or a sensor, is characterized by a set of parameters, interacts with a measurement apparatus (MA), and then is postselected onto a set of orthonormal final states. Measurements of the MA yield an estimation of the parameters. We first derive classical and quantum Cramér–Rao lower bounds and then discuss their archivable condition and the trade-offs in the postselection measurements, in general, including the case when a sensor is in a mixed state. Its whole information can, in principle, be obtained via the MA, which is not possible without postselection. We then apply the framework to simultaneous measurements of phase and its fluctuation as an example.

Quantum precision thermometry with weak measurements

As the minituarization of electronic devices, which are sensitive to temperature, grows apace, sensing of temperature with ever smaller probes is more important than ever. Genuinely quantum mechanical schemes of thermometry are thus expected to be crucial to future technological progress. We propose a new method to measure the temperature of a bath using the weak measurement scheme with a finite dimensional probe. The precision offered by the present scheme not only shows similar qualitative features as the usual Quantum Fisher Information based thermometric protocols, but also allows for flexibility over setting the optimal thermometric window through judicious choice of post selection measurements.