We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the systems state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. A discussion on the extension of the algorithm to the multilevel case is also presented.
The effect of rule (4) on a series or parallel sequence of quantum mechanical steps is to insure that a conscious observer does not skip a step. This rule effectively places the observer in continuous contact with the system. Key Words: brain states, continuous observation, conscious observer, measurement, probability current, state reduction, wave collapse.
Based on weak measurement technology, we propose the first three-observer dimension witness protocol in a prepare-and-measure setup. By applying the dimension witness inequality based on the quantum random access code and the nonlinear determinant value, we demonstrate that double classical dimension witness violation is achievable if we choose appropriate weak measurement parameters. Analysis of the results will shed new light on the interplay between the multi-observer quantum dimension witness and the weak measurement technology, which can also be applied in the generation of semi-device-in…
We investigate the trade-off between information gain and disturbance for a class of weak von Neumann measurements on spin-$\frac{1}{2}$ particles, and derive the unusual measurement pointer state that saturates this trade-off. We then consider the fundamental question of sharing the non-locality of a single particle of an entangled pair among multiple observers, and demonstrate that by exploiting the information gain disturbance trade-off, one can obtain an arbitrarily long sequence of consecutive and independent violations of the CHSH-Bell inequality.
Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have focused on a single pair of entangled particles distributed to only two separated observers. Recently, it has been shown surprisingly that multiple observers can share the nonlocality present in a single particle from an entangled pair using the method of weak measurements [Phys. Rev. Lett. {\bf 114}, 250401 (2015)]. Here we report an observation of double CHSH…
Bipartite Bell inequalities can be simultaneously violated by two different pairs of observers when weak measurements and signaling is employed. Here we experimentally demonstrate the violation of two simultaneous CHSH inequalities by exploiting a two-photon polarization maximally entangled state. Our results demonstrate that large double violation is experimentally achievable. Our demonstration may have impact for Quantum Key Distribution or certification of Quantum Random Number generators based on weak measurements.
We consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the knowledge of the measurement result can restore the pure wavefunction at any time (this can be experimentally verified). The formalism allows to write a simple Langevin equation for the random evolution of the system density matrix which is reflected and caused by the stochastic detector output. Gradual wavefunction ``collapse'' and quantum Zeno effect are naturall…
We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each observer for a maximally entangled state and two observables for a non-maximally entangled state and write down appropriate inequalities and show violation by quantum examples. Finding an example for quadratures or position and momentum is left as an open problem.
We consider a continuous-variable quantum teleportation protocol between a uniformly accelerated sender in the right Rindler wedge, a conformal receiver restricted to the future light cone, and an inertial observer in the Minkowski vacuum. Using a non-perturbative quantum circuit model, the accelerated observer interacts unitarily with the Rindler modes of the field, thereby accessing entanglement of the vacuum as a resource. We find that a Rindler-displaced Minkowski vacuum state prepared and teleported by the accelerated observer appears mixed according to the inertial observer, despite a re…
Nonlocality plays a fundamental role in quantum information science. Recently, it has been theoretically predicted and experimentally demonstrated that the nonlocality of an entangled pair may be shared among multiple observers using weak measurements with moderate strength. Here we devise an optimal protocol of nonlocality sharing among three observers and show experimentally that nonlocality sharing may be also achieved using weak measurements with near-maximum strength. Our result sheds light on the interplay between nonlocality and quantum measurements and, may find applications in quantum…
Quantum networks, which can exceed the framework of standard bell theorem, flourish the investigation of quantum nonlocality further. Recently, a concept of full quantum network nonlocality (FNN) which is stronger than network nonlocality, has been defined and can be witnessed by Kerstjens-Gisin-Tavakoli (KGT) inequalities [Phys. Rev. Lett. 128 (2022)]. In this letter, we explored the recycling of FNN as quantum resources by analyzing the FNN sharing between different combinations of observers. The FNN sharing in extended bilocal scenario via weak measurements has been completely discussed. Ac…
We consider two straightforward rules that govern the stochastic choice in a single quantum mechanical event. They are shown to lead to absurd results if an objective state reduction is allowed to compete with an observer state reduction. Since the latter collapse is empirically verifiable, the existence of the former is thrown into question. Key Words: Born Interpretation, brain states, continuous observation, conscious observer, objective measurement, observer measurement, probability current, state reduction, wave collapse.
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that for two observers undergoing finite acceleration, the entanglement vanishes between the lowest frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement i…
We study sequential state discrimination measurements performed on the same qubit by subsequent observers. Specifically, we focus on the case when the observers perform a kind of a minimum-error type state discriminating measurement where the goal of the observers is to maximize their joint probability of successfully guessing the state that the qubit was initially prepared in. We call this the joint best guess strategy. In this scheme, Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, and so on to altogether N consec…
A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced in [Cavalcanti \emph{et al.}, Phys. Rev. Lett. {\bf 99}, 210405 (2007)]. We prove that any $n$-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.
The problem of the observer in quantum mechanics is getting new human content. The paradox of Wigner's friend and its extended versions have observers who not only observe quantum phenomena, but communicate, have memories and even super-observer powers. Observers are represented by particle paths and state memories and advanced AI has been suggested to act as an observer. There is a new call for a solid theory of the observer in quantum mechanics. Two different branches of observer theories have emerged. The purely physical one is Heisenbergian, e.g. relational quantum mechanics where the obse…
Nonperturbative analysis of quantum entanglement and quantum teleportation protocol using oscillator variables carried by observers in relativistic motion under the continuous influence of the environment is given. The full time evolution of quantum entanglement among static and accelerated observers is studied. The environment plays a dual role. While it creates bipartite and tripartite entanglement among observers even when the initial state is separable, it suppresses the entanglement via decoherence. Motivated by the black hole information problem, we consider quantum teleportation between…
The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees evolution as the continuous unfolding of a canonical transformation which may be described using the two Hamiltonians. When the system is quantized both Hamiltonians become Hermitian operators in the standard positive definite inner product. Hence, each observer sees the evolution of the wave function as the continuous unfolding of a unitary transformation in…
Weak measurements can be seen as an attempt at answering the 'Which way?' question without destroying interference between the pathways involved. Unusual mean values obtained in such measurements represent the response of a quantum system to this 'forbidden' question, in which the 'true' composition of virtual pathways is hidden from the observer. Such values indicate a failure of a measurement where the uncertainty principle says it must fail, rather than provide an additional insight into physical reality.
We revisit the "counterfactual quantum communication" of Salih et al. [1], who claim that an observer "Bob" can send one bit of information to a second observer "Alice" without any physical particle traveling between them. We show that a locally conserved, massless current - specifically, a current of modular angular momentum, $L_z$ mod 2$\hbar$ - carries the one bit of information. We integrate the flux of $L_z$ mod 2$\hbar$ from Bob to Alice and show that it equals one of the two eigenvalues of $L_z$ mod 2$\hbar$, either 0 or $\hbar$, thus precisely accounting for the one bit of information …
We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Renyi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depend…
The sampled negative energy density seen by inertial observers, in arbitrary quantum states is limited by quantum inequalities, which take the form of an inverse relation between the magnitude and duration of the negative energy. The quantum inequalities severely limit the utilization of negative energy to produce gross macroscopic effects, such as violations of the second law of thermodynamics. The restrictions on the sampled energy density along the worldlines of accelerated observers are much weaker than for inertial observers. Here we will illustrate this with several explicit examples. We…
In conventional field theories, the emission of Hawking radiation in the background of a collapsing star requires transplanckian energy fluctuations. These fluctuations are encoded in the weak values of the energy-momentum operator constructed from matrix elements between both -in and -out states. It is argued that taming of these weak values by back-reaction may lead to geometrical backgrounds which are also build from weak values of the gravitational field operators. This leads to different causal histories of the black hole as reconstructed by observers crossing the horizon at different tim…
We show that long standing debates on the collapse and the role of the observer in quantum mechanics can be resolved experimentally via a nondistructive continuous monitoring of a single quantum system. An example of such a system, coupled with the point-contact detector is presented. The detailed quantum mechanical analysis of the entire system (including the detector) shows that under certain conditions the measurement collapse would generate distinctive effects in the detector behavior, which can be experimentally investigated.
