arXiv subjects

Izumi Tsutsui

Publications and source records attributed to Izumi Tsutsui.

At least 19 recordsLinked to original sources

arXiv2025

Quantum Resonance Beyond Direct Measurement: Insights from Weak Measurement

Aharonov's weak value amplification realized via weak measurement provides a versatile means to measure physical parameters with high accuracy, similar to quantum resonance epitomized by the Rabi and Ramsey resonances. The similarity between the two is not accidental: in fact, these two methods of precision measurement have recently been shown to be interconnected for the particular case of direct weak measurement. Here we show that this connection also holds in the case of indirect weak measurement, which is the standard scheme used mostly for studies of weak value amplification. We present a unified framework of weak measurements in which direct measurement appears as a special case of indirect measurement. This allows us to compare the measurement precision of different methods on a common basis, as demonstrated explicitly for the Rabi and Ramsey resonances, showing how the precision of the latter surpasses that of the former in the context of weak value amplification.

quant-ph↗

arXiv2025

Quantum Resonance viewed as Weak Measurement

Quantum resonance, i.e., amplification in transition probability available under certain conditions, offers a powerful means for determining fundamental quantities in physics, including the time duration of the second adopted in the SI units and neutron's electric dipole moment which is directly linked to CP violation. We revisit two of the typical examples, the Rabi resonance and the Ramsey resonance, and show that both of these represent the weak value amplification when involving significant enhancement of transition probabilities and that near the resonance points they share exactly the same behavior of transition probabilities except for the measurement strength whose difference leads to the known advantage of the Ramsey resonance in the sensitivity. Conversely, as a by-product of the relationship, we may measure the weak value through quantum resonance. In fact, we argue that previous measurements of neutron electric dipole moment based on the Ramsey resonance have potentially determined the weak value of neutron's spin with much higher precision than the conventional weak value measurement.

quant-ph↗

arXiv2024

Indistinguishability between quantum randomness and pseudo-randomness under efficiently calculable randomness measures

We present a no-go theorem for the distinguishability between quantum random numbers (i.e., random numbers generated quantum mechanically) and pseudo-random numbers (i.e., random numbers generated algorithmically). The theorem states that one cannot distinguish these two types of random numbers if the quantum random numbers are efficiently classically simulatable and the randomness measure used for the distinction is efficiently computable. We derive this theorem by using the properties of cryptographic pseudo-random number generators, which are believed to exist in the field of cryptography. Our theorem is found to be consistent with the analyses on the actual data of quantum random numbers generated by the IBM Quantum and also those obtained in the Innsbruck experiment for the Bell test, where the degrees of randomness of these two set of quantum random numbers turn out to be essentially indistinguishable from those of the corresponding pseudo-random numbers. Previous observations on the algorithmic randomness of quantum random numbers are also discussed and reinterpreted in terms of our theorems and data analyses.

quant-ph↗

arXiv2023

A Universal Formulation of Uncertainty Relation for Error and Disturbance

We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable. Our relation violates the traditional na{ï}ve bound $\hbar/2$ for the position-momentum measurement while respecting Heisenberg's original philosophy of the uncertainty principle. Our error-disturbance relation admits a parallel formulation to our relation for errors, which also embraces the standard Kennard--Robertson (Schr{ö}dinger) relation as a special case; this attains a unified picture of the three orthodox realms of uncertainty regarding quantum indeterminacy, measurement, and observation effect within a single framework.

quant-ph↗

arXiv2021

Weak value amplification and the lifetime of decaying particle

We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct measurement scheme presented here shows that, for simple two-level systems, the lifetime may be prolonged more than three times compared to the original one, while it can also be shortened arbitrarily by a proper choice of postselection. This result is consistent with our previous analysis on the possible prolongation of the lifetime of B mesons that may be observed in laboratories, and suggests room for novel applications of weak value amplification beyond precision measurement conventionally considered.

quant-ph↗

arXiv2021

Weak Value Amplification in High Energy Physics: A Case Study for Precision Measurement of CP Violation in B Meson Decays

The technique of weak value amplification, proposed by Aharonov et al. in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible by exploiting the freedom of `postselection' specifying actively the final state in the physical process. Here we report for the first time the feasibility of utilizing the technique of weak value amplification in high energy particle physics, especially in measuring the CP-violating parameters in B meson decays, where the effective lifetime of the decay mode is expected to be prolonged statistically due to the postselection. Our analysis shows that, when adopted in the Belle II experiment at the SuperKEKB collider, the effective lifetime may be prolonged up to 2.6 times, and that the measurement precision of the CP-violating parameters will also be improved by its effect.

quant-ph↗

arXiv2021

On the Feasibility of Bell Inequality Violation at ATLAS Experiment with Flavor Entanglement of $B^{0}\bar{B}^{0}$ Pairs from $pp$ Collisions

We examine the feasibility of the Bell test (i.e., detecting a violation of the Bell inequality) with the ATLAS detector in Large Hadron Collider (LHC) at CERN through the flavor entanglement between the B mesons. After addressing the possible issues that arise associated with the experiment and how they may be treated based on an analogy with conventional Bell tests, we show in our simulation study that under realistic conditions (expected from the LHC Run 3 operation) the Bell test is feasible under mild assumptions. The definitive factor for this promising result lies primarily in the fact that the ATLAS detector is capable of measuring the decay times of the B mesons independently, which was not available in the previous experiment with the Belle detector at KEK. This result suggests the possibility of the Bell test in much higher energy domains and may open up a new arena for experimental studies of quantum foundations.

hep-ph↗

arXiv2020

Uncertainty Relations of Variances in View of the Weak Value

The Schr{ö}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is derived from the former. In this paper we point out that, albeit more subtle, there is yet another inequality which underlies the Schr{ö}dinger inequality in the same sense. The key component of this observation is the use of the weak-value operator $A_{\rm w}(B)$ introduced in our previous works (named after Aharonov's weak value), which was shown to act as the proxy operator for $A$ when $B$ is measured. The lower bound of our novel inequality supplements that of the Schr{ö}dinger inequality by a term representing the discord between $A_{\rm w}(B)$ and $A$. In addition, the decomposition of the Schr{ö}dinger inequality, which was also obtained in our previous works by making use the weak-value operator, is examined more closely to analyze its structure and the minimal uncertainty states. Our results are exemplified with some elementary spin 1 and 3/2 models as well as the familiar case of $A$ and $B$ being the position and momentum of a particle.

quant-ph↗

arXiv2020

Geometric Formulation of Universally Valid Uncertainty Relation for Error

We present a new geometric formulation of uncertainty relation valid for any quantum measurements of statistical nature. Owing to its simplicity and tangibility, our relation is universally valid and experimentally viable. Although our relation violates the na{ï}ve non-commutativity bound $\hbar/2$ for the measurement of position and momentum, the spirit of the uncertainty principle still stands strong. Our relation entails, among others, the Ozawa relation as a corollary, and also reduces seamlessly to the standard Kennard-Robertson relation when the measurement is non-informative.

quant-ph↗

arXiv2019

Secure random number generation from parity symmetric radiations

The random number generators (RNGs) are an indispensable tool in cryptography. Of various types of RNG method, those using radiations from nuclear decays (radioactive RNG) has a relatively long history but their security has never been discussed rigorously in the literature. In this paper we propose a new method of the radioactive RNG that admits a simple and rigorous proof of security. The security proof is made possible here by exploiting the parity (space inversion) symmetry arising in the device, which has previously been unfocused but is generically available for a nuclide which decays by parity-conserving interactions.

quant-ph↗

arXiv2019

On the Validity of Weak Measurement Applied for Precision Measurement

We present a general framework of examining the validity of weak measurement -- the standard procedure to acquire Aharonov's weak value -- which has been used intensively in recent years for precision measurement, taking advantage of the amplification mechanism available for the weak value. Our framework allows one to deal systematically with various causes of uncertainties intrinsic to the actual measurement process as well as those found in the theoretical analysis employed to describe the system. Using our framework, we examine in detail the two seminal experiments, Hosten's detection measurement of the spin Hall effect of light and Dixon's ultra sensitive beam deflection measurement. Our analysis shows that their results are well within the range of amplification (actually in the vicinity of the optimal point) where the weak measurements are valid. This suggests that our framework is both practical and sound, and may be useful to determine beforehand the possible extent of amplification in the future weak measurement experiments.

quant-ph↗

arXiv2018

When photons are lying about where they have been

The past of the photon in a nested Mach-Zehnder interferometer with an inserted Dove prism is analyzed. It is argued that the Dove prism does not change the past of the photon. Alonso and Jordan correctly point out that an experiment by Danan et al. demonstrating the past of the photon in nested interferometer will show different results when the Dove prism is inserted. The reason, however, is not that the past is changed, but that the experimental demonstration becomes incorrect. The explanation of a signal from the place in which the photon was (almost) not present is given. Bohmian trajectory of the photon is specified.

quant-ph↗

arXiv2017

On Quantisations, Quasi-probabilities and the Weak Value

We propose a general framework of the quantum/quasi-classical transformations by introducing the concept of quasi-joint-spectral distribution (QJSD). Specifically, we show that the QJSDs uniquely yield various pairs of quantum/quasi-classical transformations, including the Wigner-Weyl transform. We also discuss the statistical behaviour of combinations of generally non-commutin quantum observables by introducing the concept of quantum correlations and conditional expectations defined analogously to the classical counterpart. Based on these, Aharonov's weak value is given a statistical interpretation as one realisation of the quantum conditional expectations furnished in our formalism.

quant-ph↗

arXiv2016

Quasi-probabilities in Conditioned Quantum Measurement and a Geometric/Statistical Interpretation of Aharonov's Weak Value

We show that the joint behaviour of an arbitrary pair of quantum observables can be described by quasi-probabilities, which are extensions of the standard probabilities used for describing the behaviour of a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov's weak value. Specifically, we present a general prescription for the construction of quasi-joint-probability (QJP) distributions associated with a given pair of observables. These QJP distributions are introduced in two complementary approaches: one from a bottom-up, strictly operational construction realised by examining the mathematical framework of the conditioned measurement scheme, and the other from a top-down viewpoint realised by applying the results of spectral theorem for normal operators and its Fourier transforms. It is then revealed that, for a pair of simultaneously measurable observables, the QJP distribution reduces to their unique standard joint-probability distribution, whereas for a non-commuting pair there exists an inherent indefiniteness in the choice, admitting a multitude of candidates that may equally be used for describing their joint behaviour. In the course of our argument, we find that the QJP distributions furnish the space of operators with their characteristic geometric structures such that the orthogonal projections and inner products of observables can, respectively, be given statistical interpretations as `conditionings' and `correlations'. The weak value $A_{w}$ for an observable $A$ is then given a geometric/statistical interpretation as either the orthogonal projection of $A$ onto the subspace generated by another observable $B$, or equivalently, as the conditioning of $A$ given $B$.

quant-ph↗

arXiv2016

Uncertainty Relations for Approximation and Estimation

We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cram{é}r-Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position-momentum and the time-energy relations in one framework albeit handled differently.

quant-ph↗

arXiv2016

Weak Value, Quasiprobability and Bohmian Mechanics

We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov's weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality.

quant-ph↗

arXiv2015

Quantum Trajectories based on the Weak Value

The notion of trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature of the value. In this paper, we explore the physical significance provided by this weak trajectory by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.

quant-ph↗

arXiv2014

Weak Value and the Wave-Particle Duality

The weak value, introduced by Aharonov et al. to extend the conventional scope of physical observables in quantum mechanics, is an intriguing concept which sheds new light on quantum foundations and is also useful for precision measurement, but it poses serious questions on its physical meaning due to the unconventional features including the complexity of its value. In this paper we point out that the weak value has a direct connection with the wave-particle duality, in the sense that the wave nature manifests itself in the imaginary part while the particle nature in the real part. This is illustrated by the double slit experiment, where we argue, with no conflict with complementarity, that the trajectory of the particle can be inferred based on the weak value without destroying the interference.

quant-ph↗