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The Born rule describes the probability of obtaining an outcome when measuring an observable of a quantum system. As it can only be tested by measuring many copies of the system under consideration, it does not hold for non-replicable…

Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…

Physics and Society · Physics 2024-12-10 Jiazhen Liu , Nathaniel M. Aden , Debasish Sarker , Chaoming Song

In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…

Quantum Physics · Physics 2025-09-17 Victor Barizien , Jean-Daniel Bancal

We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points that are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become…

Statistical Mechanics · Physics 2019-10-22 Amina Khatun , Somendra M. Bhattacharjee

Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…

Statistics Theory · Mathematics 2007-06-13 Richard D. Gill

We study a Bose-Einstein condensate at the low energy limit and show that their collective dynamics exhibit interesting quantum dynamical behavior. The system undergoes a dynamical quantum phase transition after a sudden quench into a…

Quantum Physics · Physics 2019-11-26 Mehdi Abdi

We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the…

Quantum Physics · Physics 2009-11-10 Armen E. Allahverdyan , Roger Balian , Theo M. Nieuwenhuizen

The dynamical quantum phase transition (DQPT) is an important concept in nonequilibrium critical phenomena; however, its relation to the equilibrium quantum phase transition (EQPT) remains obscure. Substantial evidence has suggested that…

Quantum Physics · Physics 2025-08-15 Yumeng Zeng , Shu Chen

We study the phase transitions induced by sequentially measuring a single qubit precessing under an external transverse magnetic field. Under projective quantum measurement, the probability distribution of the measurement outcomes can be…

Quantum Physics · Physics 2020-07-01 Xinru Tang , Fuxiang Li

Dynamical quantum phase transitions (DQPTs) have been studied in the extended XY model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical…

Statistical Mechanics · Physics 2025-09-29 Saeid Ansari , R. Jafari , Alireza Akbari , Mehdi Abdi

This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model in its infinite-size limit exhibits shape-phase transitions between spherical, deformed…

Nuclear Theory · Physics 2008-12-18 Pavel Cejnar , Jan Jolie

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium…

Statistical Mechanics · Physics 2018-04-24 Markus Heyl

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$ for each degree of freedom, we show that…

Statistical Mechanics · Physics 2019-07-29 Brian Skinner , Jonathan Ruhman , Adam Nahum

A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…

Statistical Mechanics · Physics 2016-08-31 Armen E. Allahverdyan , Roger Balian , Theo M. Nieuwenhuizen

In this paper, we construct 2-dimensional bipartite cluster states and perform single-qubit measurements on the bulk qubits. We explore the entanglement scaling of the unmeasured 1-dimensional boundary state and show that under certain…

Quantum Physics · Physics 2025-01-29 Hanchen Liu , Vikram Ravindranath , Xiao Chen

Measurement-induced phase transitions (MIPTs) epitomize new intellectual pursuits inspired by the advent of quantum hardware and the emergence of discrete and programmable circuit dynamics. Nevertheless, experimentally observing this…

Quantum Physics · Physics 2025-08-25 Hyejin Kim , Abhishek Kumar , Yiqing Zhou , Yichen Xu , Romain Vasseur , Eun-Ah Kim

We study the statistical properties of a single two-level system (qubit) subject to repetitive ancilla-based measurements. This setup is a fundamental minimal model for exploring the intricate interplay between the unitary dynamics of the…

Quantum Physics · Physics 2024-03-26 Paul Pöpperl , Igor V. Gornyi , David B. Saakian , Oleg M. Yevtushenko

While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum…

Quantum Physics · Physics 2025-05-19 Martin Weidner

The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels which…

Quantum Physics · Physics 2020-11-03 Artur Czerwinski

We review and expand on recent advances in theory and experiments concerning the problem of wavefunction uncollapse: Given an unknown state that has been disturbed by a generalized measurement, restore the state to its initial…

Quantum Physics · Physics 2010-02-18 Andrew N. Jordan , Alexander N. Korotkov