Information-Theoretical restrictions on the systems self-descriptions are applied to Quantum Measurements Theory. For the quantum object S measurement by information system O such restrictions are described by the restricted states formalism by Breuer. The analogous restrictions obtained in Algebraic QM from the analysis of Segal algebra U of O observables; O restricted states set is defined as U dual space. From Segal theorem for the associative subalgebra it's shown that such states describe the random pointer outcomes observed by O in the individual events.
By imposing system-observer symmetry on the von Neumann description of measurement, it is shown that the quantum measurement problem is structurally equivalent to a familiar reverse-engineering problem: that of describing the behavior of an arbitrary physical device as algorithm instantiation. It is suggested that this problem can at best be given a relational solution.
We present an approach based on a non-Hermitian Hamiltonian to describe the process of measurement by tunneling of a phase qubit state. We derive simple analytical expressions which describe the dynamics of measurement, and compare our results with those experimentally available.
We present a detailed description of the experiment realising for the first time a protective measurement, a novel measurement protocol which combines weak interactions with a ``protection mechanism'' preserving the measured state coherence during the whole measurement process. Furthermore, protective measurement allows finding the expectation value of an observable, i.e. an inherently statistical quantity, by measuring a single particle, without the need of any statistics. This peculiar property, in sharp contrast with the framework of traditional (projective) quantum measurement, might const…
We use a graphical representation of stabilizer states to describe, simply and efficiently, the effect of measurements of Pauli products on stabilizer states. This work complements our earlier work [Phys. Rev. A 77, 042307 (2008)], which described in graphical terms the action of Clifford operations on stabilizer states.
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being considered through the quantum-to-classical cross-over. Focusing upon projective measures, and exploiting the connection between large-$N$ quantum theories and the classical limit of related ones, we manage to push our description beyond the pre-measurement step. This allows us to show that the outcome production follows from a global-symmetry breaking, entailing the…
Another way to evaluate the spectral-correlation properties of thermal fields of solids is suggested. Such a method takes into account detailed structure of the interface transition layer separating one bulk region from those of the vacuum region. The principal element here is the surface linear response function of an arbitrary inhomogeneous electron subsystem of solids. Along with straightforward using the known response functions, for example in a hydrodynamic approach, the suggested method allows calculating the response functions self-consistently based on the time dependent density funct…
The Wigner's friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner's friend thought experiment (Frauchiger and Renner, Nature Comm. 3711, 9 (2018)) in detail and show that the reasoning process from each agent that leads to the no-go theorem is inconsistent. The inconsistency is with respect to the requirement that an agent should make use of updated information instead of outdated information. We then apply the relational formulati…
In this paper, without any priori assumption about the post-measurement state of system, we will examine how this state is restricted by assuming each of these following assumptions. First, by using this reasonable assumption that two successive measurements should be describable as one measurement. Second, by assuming the impossibility of faster than light signaling, "No-signaling condition". However, only by using these assumptions it is not possible to obtain the usual projection postulate. Instead, by means of a simple lemma, we will show that the density operator of system after a measure…
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but …
Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mec…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information transfer from A to B. We generalize this in order to explain why coherences are normally not observed in macroscopic quantum systems. Finally, we provide a quantitative insight into the balance between information gain and state disturbance. We define the quality of an information transfer. For all information transfers of a certain quality, we find a minimum…
The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation for the covariance matrix of the atomic system explicitly accounts for both the unitary evolution, the dissipation and noise due to the atom-light interaction, and the back-action due to homodyne optical detection on the beam after its interaction with the atoms. Applications to atomic spin squeezing and estimation of unknown classical parameters are presented…
Self-testing refers to the possibility of characterizing an unknown quantum device based only on the observed statistics. Here we develop methods for self-testing entangled quantum measurements, a key element for quantum networks. Our approach is based on the natural assumption that separated physical sources in a network should be considered independent. This provides a natural formulation of the problem of certifying entangled measurements. Considering the setup of entanglement swapping, we derive a robust self-test for the Bell-state measurement, tolerating noise levels up to 5%. We also di…
Self-testing, which refers to device independent characterization of the state and the measurement, enables the security of quantum information processing task certified independently of the operation performed inside the devices. Quantum states lie in the core of self-testing as key resources. However, for the different entangled states, usually different measurement settings should be taken in self-testing recipes. This may lead to the redundancy of measurement resources. In this work, we use fixed two-binary measurements and answer the question that what states can be self-tested with the s…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing state transformations both as a consequence of measurement and of dynamical evolution for a closed or open system are considered with respect to the general constraints they have to obey and their covariance properties with respect to symmetry groups. In particular different master equations are analyzed in …
Self-testing is a device-independent examination of quantum devices based on correlations of observed statistics. Motivated by elegant progresses on self-testing strategies for measurements [Phys. Rev. Lett. 121, 250507 (2018)] and for states [New J. Phys. 20, 083041 (2018)], we develop a general self-testing procedure for multipartite generalized GHZ-state measurements. The key step is self-testing all measurement eigenstates for a general N-qubit multipartite GHZ-state measurement. Following our procedure, one only needs to perform local measurements on N-2 chosen parties of the N-partite ei…
We present a protocol to perform self-stabilizing measurements on noisy qubits. We employ rapid purification in a rotating frame whose frequency is estimated and periodically updated via a Bayesian estimation scheme. The Bayesian estimation protocol employs the continuous measurement record to improve the estimate, which in turn purifies the qubit more. This procedure stabilizes the qubit. Such an adaptive measurement scheme serves the purpose of purifying the state, while minimally interfering with the phase estimation.
The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a $2 \rightarrow 1$ random access code with qubits, for which we provide analytical…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a general description of the measurement of a quantum system by a classical apparatus without running into inconsistencies. An example of classical and quantum particles interacting gravitationally is also given.
We reconsider the description for property transitions due to perfect measurements, viewing them as a special case of general transitions that are due to an externally imposed change. We propose a corresponding syntax involving operational quantum logic and a fragment of non-commutative linear logic.
There exist limits of self-inspection due to self-referential paradoxes, incompleteness and fixed point theorems. As quantum mechanics dictates the exchange of discrete quanta, measurements and self-inspection of quantized systems are fundamentally limited.
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. The extension is far from straightforward. Bes…
We consider the problem of the measurement of a system occurring during a finite time interval, while environmentally-induced noise decreases the system-state coherence. We assume a Markovian measuring device and, therefore, use a Lindbladian description for the measurement dynamics. For studying the case of noise produced by a non-Markovian environment, whose definition does not include the measuring apparatus, we use the Redfield approach to the interaction between system and environment. In the present hybrid theory, to trace out the environmental degrees of freedom, we introduce an analyti…
The bispinor wave function finds its fundamental application in the study of electrons, neutrinos and protons as particles bound by their own potentials. Classical electromagnetism and the Dirac electron theory appear to be natural extensions of the physics that rules the electron itself. However, the charge density and the negative energy eigenvalues are two concepts which cannot survive further scrutiny. The electron and the proton resemble minute planetary systems where the bispinor terms defining their physical properties revolve with definite angular momentum around the singular point of …
In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data -- qubits -- into classical data -- booleans -- . We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios\&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits wit…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian. As a specific example we consider the evolution of a quantum particle on a one-dimensional lattice that is subjected to position measurements at a specific site. By solving the corresponding non-Hermitian…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a possible integral representation of an instrument, which differs from the representations of an instrument available in the mathematical and physical literature. We introduce the notion of a quantum stochastic representation of an instrument, whose elements are wholly determined by the unitary invariants of a measuring process. We show that the description o…
Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements with detectors that are able to detect single particles. For this purpose, a detector model has been developed that can describe the time dependence of interactions between nonrelativistic particles and a detector. At the beginning of a position measurement, the detector behaves as a target consisting of a large number of quantum mechanical systems. The inciden…
High level of dissipation in normal metals makes challenging development of active and passive plasmonic devices. One possible solution to this problem is to use alternative materials. Graphene is a good candidate for plasmonics in near infrared (IR) region. In this paper we develop quantum theory of a graphene plasmon generator. We account for the first time quantum correlations and dissipation effects that allows describing such regimes of quantum plasmonic amplifier as surface plasmon emitting diode and surface plasmon amplifier by stimulated emission of radiation. Switching between these g…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the…
