Pointers for Quantum Measurement Theory (original) (raw)
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All quantum measurements can be simulated using projective measurements and postselection
2018
Implementation of generalized quantum measurements is often experimentally demanding, as it requires performing a projective measurement on a system of interest extended by the ancilla. We report an alternative scheme for implementing generalized measurements that uses solely: (a) classical randomness and post-processing, (b) projective measurements on a relevant quantum system and (c) postselection on non-observing certain outcomes. The method implements arbitrary quantum measurement in d dimensional system with success probability 1/d. It is optimal in the sense that for any dimensionn d there exist measurements for which the success probability cannot be higher. We apply our results to bound the relative power of projective and generalised measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on IBM quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements...
Universal Quantum Measurements
Journal of Physics: Conference Series, 2015
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finitedimensional quantum systems and entail the specification of only a minimal amount of structure. The first class of UQM that we consider involves the specification of the initial state of the system-no further structure is brought into play. We call operations of this type "tomographic measurements", since given the statistics of the outcomes one can deduce the original state of the system. Next, we construct a disentangling operation, the outcome of which, when the procedure is applied to a general mixed state of an entangled composite system, is a disentangled product of pure constituent states. This operation exists whenever the dimension of the Hilbert space is not a prime, and can be used to model the decay of a composite system. As another example, we show how one can make a measurement of the direction along which the spin of a particle of spin s is oriented (s = 1 2 , 1,. . .). The required additional structure in this case involves the embedding of CP 1 as a rational curve of degree 2s in CP 2s .
Von Neumann's Theory, Projective Measurement, and Quantum Computation
2014
We discuss the fact that there is a crucial contradiction within Von Neumann's theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1 ≤ N < +∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of Von Neumann's projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. We have to give up either the existence of the directions or the formalism of Von Neumann's projective measurement. Therefore, Von Neumann's theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on Von Neumann's theory. We investigate whether Von Neumann's theory meets the Deutsch-Jozsa algorithm. We discuss the fact that the crucial contradiction makes the quantum-theoretical formulation of Deutsch-Jozsa algorithm questionable. Further, we discuss the fact that projective measurement theory does not meet an easy detector model for a single Pauli observable. Especially, we systematically describe our assertion based on more mathematical analysis using raw data. We propose a solution of the problem. Our solution is equivalent to changing Planck's constant (h) to a new constant (h/ √ 2). It may be said that a new type of the quantum theory early approaches Newton's theory in the macroscopic scale than the old quantum theory does. We discuss how our solution is used in an implementation of Deutsch's algorithm.
The quantum measurement problem
International Journal of Quantum Chemistry, 2004
The measurement problem in quantum mechanics still appears to be an unresolved issue. Here we present a new quantum theory of measurement that overcomes many of the difficulties previously found. It is based on a consistent use of the linear superposition principle and distinguishes two aspects: recording and observation. A recording elicits the full interaction of the object quantum system with the quantum measuring apparatus. No wavefunction collapse is introduced. Statistics may appear at the observation of the recording only and depends on filtering processes. The theory presented here uses the existing mathematical structure of quantum mechanics but requires no ad hoc measurement postulates. Well-known paradoxical aspects in standard quantum mechanics, for instance, wave-particle duality, Schrödinger's cat, and Zeno effects do not appear in the current formulation.
The quantum measurement process: an exactly solvable model
arXiv preprint cond-mat/0309188, 2003
An exactly solvable model for a quantum measurement is discussed, that integrates quantum measurements with classical measurements. The z-component of a spin-1 2 test spin is measured with an apparatus, that itself consists of magnet of N spin-1 2 particles, coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state, according to the sign of sz of the test spin. The quantum measurement goes in two ...
Quantum States for Quantum Measurements
This work introduces a different way to understand the concept of quantum state (QS) with incidence on the concept of measurement. The mathematical architecture is unchanged; abstract QSs are elements of a linear vector space over the field of complex numbers. Inertial frames mediate introduction of configuration space (CS); the number of degrees of freedom defining the material system characterizes the CS-dimension. A rigged Hilbert space permits projecting abstract quantum states leading to generalized wave functions. CS-coordinates do not map out particle positions, wave functions retain the character of abstract quantum states; operators act on QS can yield new quantum states. Given a basis, quantum states are defined by the set of non-zero amplitudes. QSs are submitted to quantum probing; amplitudes control response to external probes. QSs are sustained by the material system yet they are not attributes (properties) of their elementary constituents; these latter must be present yet not necessarily localized. With respect to previous views on quantum measurement the one presented here shows characteristic differences, some of which are discussed below.
Decoherence bypass of macroscopic superpositions in quantum measurement
Journal of Physics A: Mathematical and Theoretical, 2008
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object-pointer entanglement and environment-induced decoherence of distinct pointer readouts to proceed simultaneously, such that mixtures of macroscopically distinct object-pointer product states arise without intervening macroscopic superpositions, and (iii) go beyond the Markovian treatment of decoherence.
1999
In former work, quantum computation has been shown to be a problem solving process essentially affected by both the reversible dynamics leading to the state before measurement, and the logical-mathematical constraints introduced by quantum measurement (in particular, the constraint that there is only one measurement outcome). This dual influence, originated by independent initial and final conditions, justifies the quantum computation speed-up and is not representable inside dynamics, namely as a one-way propagation. In this work, we reformulate von Neumann's model of quantum measurement at the light of above findings. We embed it in a broader representation based on the quantum logic gate formalism and capable of describing the interplay between dynamical and non-dynamical constraints. The two steps of the original model, namely (1) dynamically reaching a complete entanglement between pointer and quantum object and (2) enforcing the one-outcome-constraint, are unified and reve...
The Quantum Measurement Problem: State of Play
This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don’t advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the “traditional” formulation of the problem.