What belongs to quantum theory is no more than what is needed for its derivation. We argue for an approach focusing on reconstruction rather than interpretation of quantum mechanics and analyze several examples of reconstruction. We submit that reconstruction advances our understanding of quantum theory irrespective of one's ontological stance.
We introduce a new notion of entropy for quantum states, called contextual entropy, and show how it unifies Shannon and von Neumann entropy. The main result is that from the knowledge of the contextual entropy of a quantum state of a finite-dimensional system, one can reconstruct the quantum state, i.e., the density matrix, if the Hilbert space is of dimension 3 or greater. We present an explicit algorithm for this state reconstruction and relate our result to Gleason's theorem.
Quantum logic understood as a reconstruction program had real successes and genuine limitations. This paper offers a synopsis of both and suggests a way of seeing quantum logic in a larger, still thriving context.
We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to arbitrary number of users is generated at each port by ensemble of known quantum states with assistance of classical information of measurement outcomes by broadcasting. The obtained quantum state for each user is optimal in the sense that the fidelity universally achieves the upper bound. We present the universal quantum state distribution by providing physical r…
The number of measurements required to reconstruct the states of quantum systems increases exponentially with the quantum system dimensions, which makes the state reconstruction of high-qubit quantum systems have a great challenge in physical quantum computing experiments. Compressive sensing (CS) has been verified as a effective technique in the reconstruction of quantum state, however, it is still unknown that if CS can reconstruct quantum states given the less data measured by nuclear magnetic resonance (NMR). In this paper, we propose an effective NMR quantum state reconstruction method ba…
Reconstruction of large-sized data from small-sized ones is an important problem in information science, and a typical example is the image super-resolution reconstruction in computer vision. Combining machine learning and quantum computing, quantum machine learning has shown the ability to accelerate data processing and provides new methods for information processing. In this paper, we propose two frameworks for data reconstruction based on quantum neural networks (QNNs) and quantum autoencoder (QAE). The effects of the two frameworks are evaluated by using the MNIST handwritten digits as dat…
We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB-projectors) as input states for a D-dimensional quantum system, with D being a power of a prime number. This approach connects the results of quantum-state tomography using mutually unbiased bases (MUB) with the coefficients of a quantum process, expanded in terms of MUB-projectors. We also study the performance of the reconstruction scheme against random errors when measuring probabilities at the MUB-projectors.
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging known as Computer Aided Tomography. We explain how this method can be taken over to quantum mechanics, where it leads to a description of the quantum state in terms of the Wigner function which, although may take on negative values, plays the role of the probability density in phase space in classical physics. We explain another approach to quantum state re…
A review is given on phase-sensitive measurements, such as homodyne detection, for radiation fields and material systems. Methods of quantum-state reconstruction are considered for radiation fields, including multimode and pulsed radiation. For matter systems, methods are reported for the reconstruction of quantum states of molecular vibrations, the quantized motion of trapped atoms, Bose-Einstein condensates, atomic matter waves, electron motion, spin and angular momentum systems, and crystal lattices.
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the field, like cloning, teleportation, state estimation...). The second part is devoted to a detailed introduction to the topic of quantum correlations, covering the evidence for failure of alternative theories, some aspects of the formalism of no-signaling probability distributions and some hints towards some current research topics in the field.
We formulate a general principle that supplants a Boolean σ-algebra of intrinsic properties of a classical system by a σ-complex (a union of σ-algebras) of extrinsic properties of a quantum system that are elicited by interactions with other systems. We apply the canonical definitions of the concepts of classical physics of observables, states, combined systems, symmetries, and dynamics to derive the standard quantum characterizations, including the Schrödinger equation and the von Neumann-Lüder's Projection Rule. This manifestly consistent reconstruction of quantum mechanics is then used to d…
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of…
A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The role played by postselecting measured data will be particularly emphasized in the proposed setup, which is based on an interferometer just using simple homodyne detection.
We revisit the problem of quantum state reconstruction of light beams from the photocurrent quantum noise. As is well-known, but often overlooked, two longitudinal field modes contribute to each spectral component of the photocurrent (sideband modes). We show that spectral homodyne detection is intrinsically incapable of providing all the information needed for the full reconstruction of the two-mode spectral quantum state. Such a limitation is overcome by the technique of resonator detection. A detailed theoretical description and comparison of both methods is presented, as well as an experim…
Analysis of state reconstruction both classical and quantum mechanical on equal footing is outlined. The meaning of "mutual unbiased bases" (MUB) of Hilbert spaces is explained in detail. An alternative quantum state reconstruction, that utilizes mutual unbiased bases (MUB), is given. The MUB approach is then used for state reconstruction in a finite, d, dimensional Hilbert spaces.
The knowledge of the density matrix of a quantum state plays a fundamental role in several fields ranging from quantum information processing to experiments on foundations of quantum mechanics and quantum optics. Recently, a method has been suggested and implemented in order to obtain the reconstruction of the diagonal elements of the density matrix exploiting the information achievable with realistic on/off detectors, e.g. silicon avalanche photo-diodes, only able to discriminate the presence or the absence of light. The purpose of this paper is to provide an overview of the theoretical and e…
In continuous-variable tomography, with finite data and limited computation resources, reconstruction of a quantum state of light is performed on a finite-dimensional subspace. No systematic method was ever developed to assign such a reconstruction subspace---only ad hoc methods that rely on hard-to-certify assumptions about the source and strategies. We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace for any given unknown quantum state of light and measurement scheme. This procedure makes use of the celebrated statisti…
Modelling quantum devices is to find a model according to quantum theory that can explain the result of experiments in a quantum device. We find that usually we cannot correctly identify the model describing the actual physics of the device regardless of the experimental effort given a limited set of operations. According to sufficient conditions that we find, correctly reconstructing the model requires either a particular set of pure states and projective measurements or a set of evolution operators that can generate all unitary operators.
Simultaneous reconstruction of quantum process and noise via corrupted sensing
Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology（北京理工大学物理学院先进光电量子架构与测量教育部重点实验室）
