Quantum entanglement is the strange phenomenon first described by Einstein, Podolsky and Rosen in their famous EPR paradox paper. The document, which describes the instantaneous correlation between two particles with spacelike separation when one of the pair is measured by an observer, was meant to criticize quantum theory and regard it incomplete. Antipodal to its objective, entanglement became one of the strengths of quantum mechanics through the proposal of John Bell and the empirical results from the work of Alain Aspect, John Clauser and Anton Zeilinger disproving hidden variables within local realism. Despite these culminations, the “measurement problem” and the “quantum collapse” debates still haunt the physics community. Quantum collapse is so far interpreted as a statistical update rather than a physical occurrence to maintain the relativistic laws in check. With the rising trends and investments in quantum technological research and development in the areas of computation, communication, metrology and sensing, the exploitation of entanglement is indispensable. There is limited research in exploring entanglement dynamics through local subsystem continuous weak measurement with feedback mechanisms. Local measurement with joint correlation inference is a subject of controversy, particularly pertaining to the no signalling theorem. Compliance to this theorem can be achieved through statistics i.e. inference through repeated experimentation thereby keeping causality intact. This thesis proposes a novel method to explore the operational accessibility of local entangled quantum systems. A 4-model approach explores the behaviour of the individual and ensemble trajectories of an entangled system’s temporal evolution. The experimental design uses Kraus operators; the Stochastic Master Equation (SME) and the Lindblad Master Equation (LME) combined with quantum circuit and noise simulations to generate the needed conditional and unconditional statistics of individual and ensemble trajectories of open quantum systems via continuous weak measurement with feedback control. The Operational Accessibility Metric (OAM) defines the quantification to establish reconstruction of local system dynamics by repeated extraction of remote stochastic weak measurement record of the density matrix. The results show Root-Mean-Square Error RMSE values ranging from 0.013706 to 0.231122 and fidelities F(ρ,σ) >0.990 which are accompanied by corresponding Reconstruction Improvement Metric Γrec values from 22.3% to 71.8% correspondingly. These corollaries are supported by p-values with lowest registering at 5.19 x 10-27 and with as high as 0.008083 which still concludes the null hypothesis statistically insignificant. To further strengthen the acceptance of the alternative hypothesis, Cohen’s d effect size and statistical power has been measured indicating effect sizes as high as -7.178 and power >0.999. The experimental results validates that local dynamics is operationally accessible with significant improvement using continuous weak measurement and open feedback control.
Quantum entanglement is the strange phenomenon first described by Einstein, Podolsky and Rosen in their famous EPR paradox paper. The document, which describes the instantaneous correlation between two particles with spacelike separation when one of the pair is measured by an observer, was meant to criticize quantum theory and regard it incomplete. Antipodal to its objective, entanglement became one of the strengths of quantum mechanics through the proposal of John Bell and the empirical results from the work of Alain Aspect, John Clauser and Anton Zeilinger disproving hidden variables within local realism. Despite these culminations, the “measurement problem” and the “quantum collapse” debates still haunt the physics community. Quantum collapse is so far interpreted as a statistical update rather than a physical occurrence to maintain the relativistic laws in check. With the rising trends and investments in quantum technological research and development in the areas of computation, communication, metrology and sensing, the exploitation of entanglement is indispensable. There is limited research in exploring entanglement dynamics through local subsystem continuous weak measurement with feedback mechanisms. Local measurement with joint correlation inference is a subject of controversy, particularly pertaining to the no signalling theorem. Compliance to this theorem can be achieved through statistics i.e. inference through repeated experimentation thereby keeping causality intact. This thesis proposes a novel method to explore the operational accessibility of local entangled quantum systems. A 4-model approach explores the behaviour of the individual and ensemble trajectories of an entangled system’s temporal evolution. The experimental design uses Kraus operators; the Stochastic Master Equation (SME) and the Lindblad Master Equation (LME) combined with quantum circuit and noise simulations to generate the needed conditional and unconditional statistics of individual and ensemble trajectories of open quantum systems via continuous weak measurement with feedback control. The Operational Accessibility Metric (OAM) defines the quantification to establish reconstruction of local system dynamics by repeated extraction of remote stochastic weak measurement record of the density matrix. The results show Root-Mean-Square Error RMSE values ranging from 0.013706 to 0.231122 and fidelities F(ρ,σ) >0.990 which are accompanied by corresponding Reconstruction Improvement Metric Γrec values from 22.3% to 71.8% correspondingly. These corollaries are supported by p-values with lowest registering at 5.19 x 10-27 and with as high as 0.008083 which still concludes the null hypothesis statistically insignificant. To further strengthen the acceptance of the alternative hypothesis, Cohen’s d effect size and statistical power has been measured indicating effect sizes as high as -7.178 and power >0.999. The experimental results validates that local dynamics is operationally accessible with significant improvement using continuous weak measurement and open feedback control.
A local measurement on one member of an entangled composite system is said to change the distant member's state instantaneously. Taken without qualification, this is misleading. A selective measurement changes the conditional state assigned to the remote subsystem once a local outcome is specified; a non-selective measurement, where that outcome is ignored, leaves the remote reduced density operator unchanged. This distinction reconciles quantum state update with operational no-signalling and provides the setting for Einstein–Podolsky–Rosen steering. This review develops measurement using density operators, completely positive instruments, Kraus representations, partial traces, conditional states, and steering assemblages. It derives the invariance of remote marginal statistics under local trace-preserving operations and contrasts this with Bell-local factorization. It examines the hierarchy among entanglement, steering, and Bell nonlocality, joint measurability, remote state preparation, and one-sided device-independent protocols. The article considers spacelike-separated measurements, microcausality in relativistic quantum theory, and ontological readings of selective state update offered by Everettian, Bohmian, collapse, and relational approaches. Decoherence is treated as the process through which local outcomes become records, while quantum Darwinism accounts for their redundant local accessibility. It highlights gaps in literature, and concludes that entanglement permits nonclassical conditional correlations, but local measurement supplies no controllable superluminal signal.
Measurement and control of quantum systems play an important role in science and technology, from the foundations of quantum mechanics to practical applications. This thesis presents theoretical and experimental work that exploits quantum measurement and measurement-based feedback control to study some new problems in the contexts of solid state physics and optical quantum systems. In the first part, we consider the dynamics of open quantum systems conditioned on continuous measurements. We revisit the fact that dynamical quantum events are detector dependent by framing the problem as a quantum correlation test of the Einstein-Podolsky-Rosen (EPR) steering type. In this regards, a no-go theorem for quantum diusion is derived. In order to study a realistic experimental situation we scrutinise dierent physical systems, Einstein-Podolsky-Rosen steering inequalities and measurement protocol. We show that the no-go result for quantum diusion is not universal and does not apply to quantum jumps by devising a novel adaptive measurement scheme. Since the objectiveness of pure-state dynamical models is ruled out by quantum entanglement, then it is reasonable to say that quantum jumps are more quantum than quantum diusion. In the rst part we also study a stochastic feedback control of quantum transport. We show that using a feedback control strategy it is possible to restrict the dynamics of a double quantum dot system to a non-orthogonal two-state ensemble. The feedback control approach can be less experimentally challenging than an adaptive measurement scheme, as the latter requires implementing local oscillators, which might be dicult to realise in mesoscopic physics.
Despite its remarkable success in describing microscopic phenomena, quantum mechanics continues to pose unresolved foundational questions concerning measurement, nonlocality, wavefunction collapse, and the nature of physical reality. These issues were highlighted by the EPR paradox. Quantum mechanics predicts that measuring one particle’s observable instantaneously determines the state of the other, seemingly violating special relativity’s prohibition of faster-than-light influences and suggesting an incomplete description of physical reality. However, Bell’s theorem has largely ruled out local hidden variable theories. In this paper, I critically examine the assumptions in deriving Bell’s theorem and demonstrate that the theorem does not apply strictly to quantum mechanics. By assuming measurement is always accompanied by uncontrollable environment interactions, I show that quantum theory can be local and realism with decoherence in EPR-like measurement. Specifically, I apply the quantum decoherence framework, pioneered by Zeh, Zurek and Leggett to analyze an EPR-like system using system-environment interactions as a measurement model. The results illustrate that measurement on one entangled particle does not instantaneously collapse the system's wavefunction. Instead, the local wavefunctions of the measured particle and its environment evolve dynamically, while the remote particle’s wavefunction remains unchanged. Environment-induced decoherence selects pointer states and rapidly suppresses quantum correlations through strictly local interactions, giving rise to the appearance of wavefunction collapse. These findings challenge the conventional interpretation of Bell’s theorem and suggest that quantum mechanics fundamentally respects locality and realism if the wavefunction is treated as an ontic entity. This work offers a potential path toward a locally realistic quantum theory in alignment with Einstein’s vision. It not only strengthens the conceptual foundations of quantum mechanics, but also carries tremendous implications for quantum information processing and computing.
Quantum entanglement is an essential principle in quantum mechanics, illustrating the relationship between two or more spatially separated particles.This correlation has been experimentally proven through various techniques, including the entangled photon experiment. Furthermore, the breach of Bell's inequality has confirmed that entanglement represents a genuine physical occurrence, which cannot be accounted for by local hidden variables, thus highlighting the peculiar characteristics of quantum mechanics. This article aims to introduce quantum entanglement and Bell's inequality, and to discuss the experiments conducted by Alain Aspect, John Clauser, and Anton Zeilinger, which paved the way for the development of quantum information science. Additionally, this paper will explore the potential applications of quantum technology in communication, cryptography, and computing, which rely on the exceptional properties of entanglement.
While Bell nonlocality can be explained through mechanisms such as retrocausality and superluminal influences, it is not clear why such mechanisms do not manifest at an everyday macroscopic level. In this paper, we show how measurement and nonlocality can be explained consistently with macroscopic realism and no-signaling, and causal relations for macroscopic quantities. Considering the measurement of a field amplitude x ̂ , we derive theorems that lead to an equivalence between a quantum phase-space probability distribution Q ( x , p , t ) and stochastic trajectories for real amplitudes x ( t ) and p ( t ) propagating backward and forward in time, respectively. We present forward-backward stochastic simulations that motivate a Q -based objective-field model of reality. Amplification plays a key role in the measurement. With amplification, similar to decoherence, contributions due to interference become unobservable, leading to “branches” in x that correspond to distinct eigenvalues λ . This elucidates how the system evolves from a superposition to an eigenstate, from which Born's rule follows. For superposition states, we find that the backward and forward trajectories are connected, leading to “hidden loops.” We deduce a hybrid causal structure involving causal deterministic relations for amplified variables, along with microscopic noise inputs and hidden loops for unobservable quantities. Causal consistency is confirmed, removing grandfather-type paradoxes. The simulations allow evaluation of a state inferred for the system, conditioned on a particular branch λ , from which we deduce a model for projection and the collapse of the wave function. The theory is extended to Einstein-Podolsky-Rosen correlations and Bell nonlocality. We demonstrate consistency with three weak local realistic premises: (1) the existence of real properties (defined for the system after operations that fix measurement settings); (2) a partial locality implying no-signaling; (3) “elements of reality” that apply to the predictions of a system by a meter, once meter settings are fixed. A Q -based hidden variable model and mechanism for Bell nonlocality is identified. Our work shows how forward-backward stochastic simulations lead to a hybrid causal structure, involving both deterministic causal relations and “hidden” stochastic loops, explaining measurement and entanglement, with paradoxes typically associated with retrocausality avoided.
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced in irreducible random way.