Reality, Measurement, and the State of the System in Quantum Mechanics

1951 ◽  
Vol 18 (4) ◽  
pp. 273-299 ◽  
Author(s):  
Edwin C. Kemble
Keyword(s):  
Quantum Mechanics ◽  
The State

scholarly journals Preparation of States in Open Quantum Mechanics

2011 ◽  
Vol 18 (03) ◽  
pp. 253-260 ◽  
Author(s):  
Kavan Modi
Keyword(s):  
Quantum Mechanics ◽  
Indirect Effects ◽  
The State ◽  
Preparation Procedure ◽  
Open Quantum ◽  
Markovian Systems ◽  
State Of The Environment

We study preparation of states for open quantum mechanics. For non-Markovian systems that are initially correlated with the environment, the effects of the preparation procedure are nontrivial. This is due to the indirect effects on the state of the environment induced via the correlations with the system and the act of preparation on the system. We give three concrete examples of preparation procedure to elucidate our claims.

Quantenmechanik und Objektivierbarkeit/ Quantum Mechanics and Objective Reality

1970 ◽  
Vol 25 (12) ◽  
pp. 1954-1957 ◽  
Author(s):  
K. Baumann
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
State Vector ◽  
The State ◽  
Measuring Apparatus ◽  
Measuring Process ◽  
Objective Reality ◽  
Objective Description ◽  
The Universe

Abstract Quantum Mechanics and Objective Reality A Schrödinger function (or a density matrix) can he ascribed only to an object whose isolation time is larger than its time of revolution. This condition can never be satisfied for macroscopic bodies. Consequently, the "cut" between object and observer must not separate a macroscopic body (measuring apparatus) from the rest of the universe. Hence in an analysis of the measuring process, the state vector of the universe must be introduced. An interpretation of this state vector is given which provides an objective description of nature.

scholarly journals Measurement theory in classical mechanics

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
So Katagiri
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Uncertainty Relation ◽  
Measurement Theory ◽  
Classical Mechanics ◽  
The State ◽  
Measurement Device ◽  
Von Neumann ◽  
Relative Interpretation ◽  
Classical And Quantum Mechanics

Abstract We investigate measurement theory in classical mechanics in the formulation of classical mechanics by Koopman and von Neumann (KvN), which uses Hilbert space. We show a difference between classical and quantum mechanics in the “relative interpretation” of the state of the target of measurement and the state of the measurement device. We also derive the uncertainty relation in classical mechanics.

EPR Elements of Physical Reality in Quantum Mechanics

1997 ◽  
Vol 12 (29) ◽  
pp. 5289-5303
Author(s):  
V. K. Thankappan ◽  
Ravi K. Menon
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Singlet State ◽  
Physical Reality ◽  
The State ◽  
Wave Functions ◽  
Definition Of

The concept of elements of physical reality (e.p.r.) in quantum mechanics as defined by Einstein, Podolsky and Rosen (EPR) is discussed in the context of the EPR–Bohm and the EPR–Bell experiments on a pair of spin 1/2 particles in the singlet state. It is argued that EPR's definition of e.p.r. is appropriate to the EPR–Bell experiment rather than to the EPR–Bohm experiment, and that Bohr's interpretation of e.p.r. is also consistent with such a viewpoint. It is shown that the observed correlation between the spins of the two particles in the EPR–Bell experiment is just a manifestation of the correlation that exists between the wave functions of the particles in the singlet state and a consequence of the fact that a Stern–Gerlach magnet does not change the state of a particle but only transforms its wave function into a representation defined by the axis of the magnet. As such, the correlation is suggested to be an affirmation of Einstein's concept of locality, and not an evidence for nonlocality.

scholarly journals Self-consistent tomography and measurement-device independent cryptography

2020 ◽  
pp. 2040003
Author(s):  
I. D. Moore ◽  
S. J. van Enk
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
The State ◽  
Correlated Errors ◽  
Measurement Device ◽  
State Preparation ◽  
Self Consistent ◽  
Average State ◽  
Measurement Device Independent ◽  
Joint State

A recurring problem in quantum mechanics is to estimate either the state of a quantum system or the measurement operator applied to it. If we wish to estimate both, then the difficulty is that the state and the measurement always appear together: to estimate the state, we must use a measurement; to estimate the measurement operator, we must use a state. The data of such quantum estimation experiments come in the form of measurement frequencies. Ideally, the measured average frequencies can be attributed to an average state and an average measurement operator. If this is not the case, we have correlated state-preparation-and-measurement (SPAM) errors. We extend some tests developed to detect such correlated errors to apply to a cryptographic scenario in which two parties trust their individual states but not the measurement performed on the joint state.

scholarly journals The fundamental connections between classical Hamiltonian mechanics, quantum mechanics and information entropy

2020 ◽  
Vol 18 (01) ◽  
pp. 1941025
Author(s):  
Gabriele Carcassi ◽  
Christine A. Aidala
Keyword(s):  
Quantum Mechanics ◽  
Information Entropy ◽  
Quantum Systems ◽  
The State ◽  
Hamiltonian Mechanics ◽  
Internal Dynamics ◽  
Classical Systems ◽  
Arbitrary Precision

We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while quantum systems can be considered the ones where the internal dynamics cannot be accessed at all. As information entropy can be used to characterize how much the state of the whole system identifies the state of its parts, classical systems can have arbitrarily small information entropy while quantum systems cannot. This provides insights that allow us to understand the analogies and differences between the two theories.

Qubits and the Framework of Quantum Mechanics

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Information ◽  
State Space ◽  
Quantum Physics ◽  
Complex Hilbert Space ◽  
The State ◽  
Mathematical Framework ◽  
Infinite Dimensional

In this section we introduce the framework of quantum mechanics as it pertains to the types of systems we will consider for quantum computing. Here we also introduce the notion of a quantum bit or ‘qubit’, which is a fundamental concept for quantum computing. At the beginning of the twentieth century, it was believed by most that the laws of Newton and Maxwell were the correct laws of physics. By the 1930s, however, it had become apparent that these classical theories faced serious problems in trying to account for the observed results of certain experiments. As a result, a new mathematical framework for physics called quantum mechanics was formulated, and new theories of physics called quantum physics were developed in this framework. Quantum physics includes the physical theories of quantum electrodynamics and quantum field theory, but we do not need to know these physical theories in order to learn about quantum information. Quantum information is the result of reformulating information theory in this quantum framework. We saw in Section 1.6 an example of a two-state quantum system: a photon that is constrained to follow one of two distinguishable paths. We identified the two distinguishable paths with the 2-dimensional basis vectors and then noted that a general ‘path state’ of the photon can be described by a complex vector with |α0|2 +|α1|2 = 1. This simple example captures the essence of the first postulate, which tells us how physical states are represented in quantum mechanics. Depending on the degree of freedom (i.e. the type of state) of the system being considered, H may be infinite-dimensional. For example, if the state refers to the position of a particle that is free to occupy any point in some region of space, the associated Hilbert space is usually taken to be a continuous (and thus infinite-dimensional) space. It is worth noting that in practice, with finite resources, we cannot distinguish a continuous state space from one with a discrete state space having a sufficiently small minimum spacing between adjacent locations. For describing realistic models of quantum computation, we will typically only be interested in degrees of freedom for which the state is described by a vector in a finite-dimensional (complex) Hilbert space.

scholarly journals Knowledge of Quantum Hidden Variables Enables Backwards-In-Time Signaling

2021 ◽  
Vol 11 (10) ◽  
pp. 4477
Author(s):  
Avishy Carmi ◽  
Eliahu Cohen ◽  
Lorenzo Maccone ◽  
Hrvoje Nikolić
Keyword(s):  
Quantum Mechanics ◽  
Reference Frame ◽  
Hidden Variables ◽  
Bohmian Mechanics ◽  
The State ◽  
Bell’S Theorem ◽  
Relativity Theory ◽  
Bell's Theorem ◽  
Preferred Reference Frame ◽  
Superluminal Signaling

Bell’s theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden variables would permit superluminal communication. Such superluminal signaling, akin to the existence of a preferred reference frame, is to be expected. However, here we provide a protocol that allows an observer with knowledge of the hidden variables to communicate with her own causal past, without superluminal signaling. That is, such knowledge would contradict causality, irrespectively of the validity of relativity theory. Among the ways we propose for bypassing the paradox there is the possibility of hidden variables that change their values even when the state does not, and that means that signaling backwards in time is prohibited in Bohmian mechanics.

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