Celebrating a Century
of Quantum Discoveries

Advancing Quantum Research Through Open Access Publishing.

Intro Image

The formal development of quantum mechanics began in 1925 with Werner Heisenberg’s matrix formulation, laying the foundation for a revolutionary understanding of the physical world. Over the past century, quantum theory has become central to modern physics, driving advances in quantum computing, cryptography, and materials science.

As quantum research continues to grow in complexity and significance, open access publishing plays a critical role in accelerating scientific progress. At MDPI, we are committed to ensuring the latest advances in quantum mechanics are freely accessible to the global research community—fostering collaboration, transparency, and innovation across disciplines.

Take a scroll down memory lane with us to discover the marvels of quantum physics since before 1925.

Special Issues

Topics

Quantum Information and Quantum Computing, 2nd Volume

Topic Editors: Durdu Guney and David Petrosyan

Abstract Submission Deadline:

31 March 2025

Manuscript Submission Deadline:

06 January 2026

Quantum Wireless Sensing

Topic Editors: Deepak Mishra, Chao Cai and Jie Zhang

Abstract Submission Deadline:

28 February 2026

Manuscript Submission Deadline:

30 April 2026

Theoretical, Quantum and Computational Chemistry—2nd Edition

Topic Editors: Jorge Garza and Andrei L. Tchougréeff

Abstract Submission Deadline:

31 March 2026

Manuscript Submission Deadline:

31 July 2026

Quantum Systems and Their Applications

Topic Editors: Chao Zheng and Jim Freericks

Abstract Submission Deadline:

15 December 2025

Manuscript Submission Deadline:

28 February 2026

Research Highlight

Review

A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies

Robert WinklerMiguel CiriaMargaret Ahmad
+2 authors

Abstract: Magnetism plays a pivotal role in many biological systems. However, the intensity of the magnetic forces exerted between magnetic bodies is usually low, which demands the development of ultra-sensitivity tools for proper sensing. In this framework, magnetic force microscopy (MFM) offers excellent lateral resolution and the possibility of conducting single-molecule studies like other single-probe microscopy (SPM) techniques. This comprehensive review attempts to describe the paramount importance of magnetic forces for biological applications by highlighting MFM’s main advantages but also intrinsic limitations. While the working principles are described in depth, the article also focuses on novel micro- and nanofabrication procedures for MFM tips, which enhance the magnetic response signal of tested biomaterials compared to commercial nanoprobes. This work also depicts some relevant examples where MFM can quantitatively assess the magnetic performance of nanomaterials involved in biological systems, including magnetotactic bacteria, cryptochrome flavoproteins, and magnetic nanoparticles that can interact with animal tissues. Additionally, the most promising perspectives in this field are highlighted to make the reader aware of upcoming challenges when aiming toward quantum technologies.

Published on 18 September 2023

Paper image for A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies
Review

Contextuality, Complementarity, Signaling, and Bell Tests

Andrei Khrennikov

Abstract: This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities.

Published on 28 September 2022

Article

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

Federico GerbinoPierre Le DoussalGuido GiachettiAndrea De Luca

Abstract: We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λÎČ)=O(Γt/n), but fluctuations ∌O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.

Published on 16 May 2024

Paper image for A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

History of Quantum Mechanics

Image for (1900) The Ultraviolet Catastrophe and Planck’s Solution

(1900) The Ultraviolet Catastrophe and Planck’s Solution

Max Planck proposed the quantum hypothesis to explain the blackbody radiation problem and introduced the concept of "energy quantization" for the first time.

This revolutionary idea laid the foundation for quantum mechanics, introducing the concept that energy levels in nature are quantized rather than continuous.

Image for (1905) Einstein’s Photoelectric Effect and Wave-Particle Duality

(1905) Einstein’s Photoelectric Effect and Wave-Particle Duality

Albert Einstein extended Planck’s ideas. He proposed the light quantum hypothesis (photon) to explain the photoelectric effect and further support the quantum concept.

Image for (1913) Bohr’s Quantum Model of the Atom

(1913) Bohr’s Quantum Model of the Atom

Niels Bohr proposed the Bohr model of the atomic structure, introducing quantization conditions into atomic orbitals and explaining the spectrum of hydrogen atoms, also reinforcing the necessity of quantization in atomic physics.

Image for (1925 - 1926) The Birth of Quantum Mechanics: Heisenberg and Schrödinger

(1925 - 1926) The Birth of Quantum Mechanics: Heisenberg and Schrödinger

Werner Heisenberg formulated matrix mechanics (quantum mechanics in matrix form), marking the birth of the mathematical framework of quantum mechanics. Erwin Schrödinger developed wave mechanics (Schrödinger equation), using wave functions to describe quantum states, which was later proved to be equivalent to matrix mechanics.

This new framework replaced classical determinism with a probabilistic view of nature, fundamentally altering our understanding of atomic and subatomic behavior and paving the way for modern quantum physics.

Image for (1927) A Significant Turning Point in the Understanding of Quantum Mechanics

(1927) A Significant Turning Point in the Understanding of Quantum Mechanics

Heisenberg proposed the uncertainty principle, which showed that it is impossible to accurately measure the position and momentum of a particle at the same time and became a cornerstone of the Copenhagen interpretation of quantum mechanics.

Bohr proposed the complementarity principle at the Solvay Conference, which led to the Copenhagen interpretation (the standard interpretation of quantum mechanics).

This year marked a significant turning point in the understanding of quantum mechanics, leading to profound insights into the nature of reality at the atomic and subatomic levels.

Image for (1928) Dirac’s Relativistic Quantum Mechanics and Antimatter Prediction

(1928) Dirac’s Relativistic Quantum Mechanics and Antimatter Prediction

Paul Dirac combined quantum mechanics and relativity to propose relativistic quantum mechanics (Dirac equation).

The Dirac equation elegantly combined quantum mechanics with special relativity, resolving inconsistencies between the two theories and introducing the concept of negative energy states.

Image for (1935) The EPR Paradox and Quantum Entanglement

(1935) The EPR Paradox and Quantum Entanglement

Albert Einstein, Boris Podolsky, and Nathan Rosen published a paper challenging the completeness of quantum mechanics, introducing what became known as the EPR paradox. They argued that certain pairs of physical properties, such as position and momentum, could not be precisely measured simultaneously, leading them to believe that quantum theory was incomplete. The EPR paradox remains a cornerstone of quantum physics, challenging our understanding of reality and sparking ongoing research into the nature of quantum entanglement and its potential applications.

Image for (1940s - 1950) Quantum Electrodynamics (QED) and Renormalization

(1940s - 1950) Quantum Electrodynamics (QED) and Renormalization

Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga developed quantum electrodynamics (QED), a quantum field theory describing how light and matter interact, to solve the problem of electromagnetic interaction.

QED became the first quantum field theory to achieve precise agreement with experimental results, setting the stage for the development of the Standard Model of particle physics.

Image for (1981 - Present) Quantum Computing and the Future

(1981 - Present) Quantum Computing and the Future

In 1981, Richard Feynman proposed a model for a "quantum computer" to simulate quantum systems and proposed the concept of quantum computing.

This idea kicked off the work to develop quantum algorithms, and marks the ongoing evolution of quantum technologies.

Image for (2025) Celebrating a Century of Quantum Discoveries

(2025) Celebrating a Century of Quantum Discoveries

Today, quantum science and technology are rapidly evolving, moving from research labs to industrial applications such as cryptography, optimization, and materials science. In 2025, the world marks the centennial of quantum mechanics.

Aligned with the International Year of Quantum Science & Technology (IYQ), MDPI proudly commemorates this occasion by highlighting our dedication to open access publishing and the dissemination of quantum research.

Journal Recommendations

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