Testing QM : the Uncertainty Principle

Universal Uncertainty Principle in Different Quantum Theories

This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in quantum physics, overcomes the difficulty that current quantum computer, quantum communication, quantum control, quantum mechanics and so on theories cannot give exact values of general uncertainty of any orders of physical quantities, further gives all relevant different expressions of the universal uncertainty principle and their applications. In fact, our st…

Considerations in the Time-Energy Uncertainty Relation from the Viewpointt of Hypothesis Testing

It is difficult to discriminate between the state of initial time $t_0$ and that of time $t_0+Δt$. The task of discriminating between the two states can be interpreted as the hypothesis testing problem as to a state $ρ$ deciding whether $ρ$ is $ρ_{t_0}$ or$ρ_{t_0+Δt}$ We show the process of optimization of this hypotheses testing and the condition that discrimination between the two states become difficult even when optimized test was executed. In addition, We consider time-enegy uncertainty relation from the viewpoint of optimized hypotheses testing. Optimization consists of two steps. The fi…

Privacy Amplification, Private States, and the Uncertainty Principle

We show that three principle means of treating privacy amplification in quantum key distribution, private state distillation, classical privacy amplification, and via the uncertainty principle, are equivalent and interchangeable. By adapting the security proof based on the uncertainty principle, we construct a new protocol for private state distillation which we prove is identical to standard classical privacy amplification. Underlying this approach is a new characterization of private states, related to their standard formulation by the uncertainty principle, which gives a more physical under…

An Uncertainty Principle For Completely Positive Maps

We present an "uncertainty principle" for quantum channels, showing a relationship between the dimensions of the range of a channel and the range of its complement. We examine some interesting specific cases, and discuss consequences for privacy of quantum channels.

Testing Heisenberg's measurement uncertainty relation of three observables

Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for contemporary researches in quantum foundations and quantum information science. Going beyond, here we report the first experimental test of MURs for three quantum observables. Following the proposal of Bush, Lahti, and Werner [Phys. Rev. A 89, 012129 (2014)], we first establish rigorously MURs for triplets of unbiased qubit observables as combined approximation errors lower-bounded by an incompatibility measure. We then develop a convex programming protocol to numerically find the exact value of t…

Comment on "Experimental realization of Popper's experiment: Violation of the uncertainty principle?"

Application of the uncertainty principle to conditional measurements is investigated, and found to be valid for measurements on separated sub-systems. In light of this, an apparent violation of the uncertainty principle obtained by Kim and Shih in their realization of Popper's experiment (quant-ph/9905039) is explained through analogy with a simple optical system.

Experimental investigation of the entanglement-assisted entropic uncertainty principle

The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in terms of entropy has been extended to the case involving quantum entanglement. With previously obtained quantum information for the particle of interest, the outcomes of both non-commuting observables can be predicted precisely, which greatly generalises the uncertainty relation. Here, we experimentally investigated the entanglement-assisted entropic uncertai…

Entanglement criterion independent on observables for multipartite Gaussian states based on uncertainty principle

The local uncertainty relation (LUR) criteria for quantum entanglement, which is dependent on chosen observables, is developed recent. In the paper, applying the uncertainty principle, an entanglement criteria for multipartite Gaussian states is given, which is implemented by a minimum optimization computer program and independent on observalbes.

Interpretation of Electron Tunneling from Uncertainty Principle

Beginners studying quantum mechanics are often baffled with electron tunneling.Hence an easy approach for comprehension of the topic is presented here on the basis of uncertainty principle.An estimate of the tunneling time is also derived from the same method.

Remarks on the Fact that the Uncertainty Principle Does Not Determine the Quantum State

We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner distributions dominated by a Gaussian and we relate this result to the coarse-graining of phase-space by "quantum blobs".

Schrodinger equation from an exact uncertainty principle

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. Thus there is an exact formulation of the uncertainty principle which precisely captures the essence of what is "quantum" about quantum mechanics.

香农熵量子纠缠判据与广义不确定性原理

Shannon Entropy Quantum Entanglement Criterion and the Generalized Uncertainty Principle

本文应用广义不确定性原理修正香农熵纠缠判据，发现其上界增大，并探讨了相关基本概念，揭示了量子引力对纠缠条件的影响。

The Uncertainty Principle of Quantum Processes

Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and quantum mechanics. The physical systems considered in the uncertainty principle are static in nature and described mathematically with a quantum state in a Hilbert space. However, many physical systems are dynamic in nature and described with the formalism of a quantum channel. In this paper, we show that the uncertainty principle can be reformulated to include p…

Uncertainty, joint uncertainty, and the quantum uncertainty principle

Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a s…

Uncertainty Principle: Classic and Quantum Aspects

Some aspects of application of the Uncertainty Principle in the range of interaction radiation with matter surveyed. The procedure of adjustment is proposed at calculation of values of an electromagnetic energy in a quantum theory of a field.

Entropy uncertainty principle for Dirac system with mass jump

Dependency on the preparation of state for the Heisenberg uncertainty principle can be removed with the help of entropy uncertainty principle. The shortness of the uncertainty principle (UP) can be overcome with the help of the concept of Shannon's information entropy (SE). In this article, we have shown that UP in terms of SE holds for a position-dependent effective mass system. We have considered the Dirac system with a mass-jump at the origin. We have proved the existence of a lower bound for a UP for this position-dependent effective mass.

Robertson-Schrödinger formulation of Ozawa's Uncertainty Principle

A more general measurement disturbance uncertainty principle is presented in a Robertson-Schrödinger formulation. It is shown that it is stronger and having nicer properties than Ozawa's uncertainty relations. In particular is invariant under symplectic transformations. One shows also that there are states of the probe (measuring device) that saturate the matrix formulation of measurement disturbance uncertainty principle.

Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle

In this work we derive a matrix formulation of a noise-disturbance uncertainty relation, which is akin to the Robertson-Schrödinger uncertainty principle. Our inequality is stronger than Ozawa's uncertainty principle and takes noise-disturbance correlations into account. Moreover, we show that, for certain types of measurement interactions, it is covariant with respect to linear symplectic transformations of the noise and disturbance operators.

Testing Generalised Uncertainty Principles through Quantum Noise

Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position-momentum commutation relations. Some of these modified relations are also consistent with general principles that may be supposed of any physical theory. Such modified commutators have significant observable consequences. Here we study the noisy behaviour of an optomechanical system assuming a certain commonly studied modified commutator. From recent observations of radiation pressure noise in tabletop optomecha…

Testing the equivalence principle through freely falling quantum objects

Free fall in a uniform gravitational field is revisited in the case of quantum states with and without classical analogue. The interplay between kinematics and dynamics in the evolution of a falling quantum test particle is discussed allowing for a better understanding of the equivalence principle at the operational level.

Generalized uncertainty principle and $D$-dimensional quantum mechanics

The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.

Bending The Heisenberg Uncertainty Principle

The celebrated Heisenberg Uncertainty Principle Δx Δp\ge \hbar/2 can allow measurement accuracies less than Δx or Δp. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a step by step process using the example of compass state, as suggested by Zurek.

Entropic uncertainty relation based on generalized uncertainty principle

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the stud…

A quantum wavelet uncertainty principle

The aim of this paper is to derive a new uncertainty principle for the generalized $q$-Bessel wavelet transform studied earlier in \cite{Rezguietal}. In this paper, an uncertainty principle associated with wavelet transforms in the $q$-calculus framework has been established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is exploited next to explore a wavelet uncertainty principle already in the $q$-calculus framework.

An Entropic Uncertainty Principle for Quantum Measurements

The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result includes not only the case of projectivmeasurements (or equivalently, observables) exhibiting degeneracy but also an uncertainty principle for a single measurement.

Directional Uncertainty Principle for Quaternion Fourier Transform

This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.

Background independent quantization and the uncertainty principle

It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to the uncertainty principle acquire a metric dependence. For Friedmann-Robertson-Walker cosmology this translates to a scale factor dependence which gives a large effect in the early universe.

On Gravity and the Uncertainty Principle

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring…

论 Wigdersons 的不确定性原理方法

On Wigdersons' approach to the uncertainty principle

本文基于 Wigdersons 的视角重新审视不确定性原理，通过引入更一般的基本不确定性原理，推导出多种新不等式并证明了作者提出的高维推广猜想。

Generalized Uncertainty Principle, Extra-dimensions and Holography

We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.

Modified entropies as the origin of generalized uncertainty principles

The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with $S_{+}$ and $S_-$ entropies are negative and posit…