Quantum trajectories based on the weak value

Mori, Takuya; Tsutsui, Izumi

doi:10.1093/ptep/ptv032

Cited by 12 publications

(11 citation statements)

References 20 publications

(47 reference statements)

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“…Some experimental and theoretical examples of other modal theories (i.e., with ontological descriptions different from the Bohmian theory, while still yielding experimental predictions identical to those of the orthodox quantum theory) can be found in Refs. [85][86][87][88]. Our paper also emphasizes that looking for a meaning of weak values without linking them to a given ontology (or mixing ontologies in a type of bipolarity that wants a reality independent of the measurement, but at the same time rejects it) is not the correct path to understand weak values.…”

Section: Discussionmentioning

confidence: 93%

Identifying weak values with intrinsic dynamical properties in modal theories

et al. 2021

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The so-called eigenvalue-eigenstate link states that no property can be associated to a quantum system unless it is in an eigenstate of the corresponding operator. This precludes the assignation of properties to unmeasured quantum systems in general. This arbitrary limitation of orthodox quantum mechanics generates many puzzling situations such as for example the impossibility to uniquely define a work distribution, an essential building block of quantum thermodynamics. Alternatively, modal theories (e.g., Bohmian mechanics) provide an ontology that always allows one to define intrinsic properties, i.e., properties of quantum systems that are detached from any possible measuring context. We prove here that Aharonov, Albert, and Vaidman's notion of a weak value can always be identified with an intrinsic dynamical property of a quantum system defined in a certain modal theory. Furthermore, the fact that weak values are experimentally accessible (as an ensemble average of weak measurements which are postselected by a strong measurement) strengthens the idea that understanding the intrinsic (unperturbed) dynamics of quantum systems is possible and useful in a given modal theory. As examples of the physical soundness of these intrinsic properties, we discuss three intrinsic Bohmian properties, viz., the dwell time, the work distribution, and the quantum noise at high frequencies.

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Section: Discussionmentioning

confidence: 93%

Identifying weak values with intrinsic dynamical properties in modal theories

et al. 2021

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“…In recent years, weak measurement has provided a method to determine a set of average trajectories for an ensemble of particles under the minimum disturbance measure process [ 8 , 9 ]. The weak values obtained by weak measurement are beyond the real eigenvalues and have complex values with their imaginary parts relating to the rate of variation in the interference observation [ 10 ]. Solid evidence of the quantum trajectory was provided by the observation of average trajectories of individual photons in a double-slits interferometer that were observed through weak measurement [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

Extending Quantum Probability from Real Axis to Complex Plane

Yang

Han

2021

Entropy

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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability Ψ2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.

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“…The significant characteristic of the weak value does not lie within the range of eigenvalues and is complex. It is pointed out that the real part of the complex weak value represents the average quantum value [8], and the imaginary part is related to the rate of variation in the interference observation [9].…”

Section: Introductionmentioning

confidence: 99%

Complex Space Nature of the Quantum World: Return Causality to Quantum Mechanics

Yang¹,

Han²

2020

Quantum Mechanics

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As one chapter, we about to begin a journey with exploring the limitation of the causality that rules the whole universe. Quantum mechanics is established on the basis of the phenomenology and the lack of ontology builds the wall which blocks the causality. It is very difficult to reconcile the probability and the causality in such a platform. A higher dimension consideration may leverage this dilemma by expanding the vision. Information may seem to be discontinuous or even so weird if only be viewed from a part of the degree of freedoms. Based on this premise, we reexamined the microscopic world within a complex space. Significantly, some knowledge beyond the empirical findings is revealed and paves the way for a more detailed exploration of the quantum world. The random quantum motion is essential for atomic particle and exhibits a wave-related property with a bulk of trajectories. It seems we can break down the wall which forbids the causality entering the quantum kingdom and connect quantum mechanics with classical mechanics. The causality returns to the quantum world without any assumption in terms of the quantum random motion under the optimal guidance law in complex space. Thereby hangs a tale, we briefly introduce this new formulation from the fundamental theoretical description to the practical technology applications.

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Quantum trajectories based on the weak value

Cited by 12 publications

References 20 publications

Identifying weak values with intrinsic dynamical properties in modal theories

Identifying weak values with intrinsic dynamical properties in modal theories

Extending Quantum Probability from Real Axis to Complex Plane

Complex Space Nature of the Quantum World: Return Causality to Quantum Mechanics

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