Uncertainty characteristics of generalized quantum measurements (original) (raw)

The Theory of Quantum Uncertainties and Quantum Measurements

  1. We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time ttt. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time t_0t_0t_0 under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove th...

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.

Information-theoretic approach to quantum error correction and reversible measurement

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We derive information-theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyze the thermodynamic cost of error correction and show that error correction can be regarded as a kind of "Maxwell demon," for which there is an entropy cost associated with information obtained from measurements performed during error correction. A prescription for thermodynamically efficient error correction is given.

Towards a new uncertainty principle: quantum measurement noise

Physics Letters A, 1991

Two generalizations of a known approach to the joint measurement of position and momentum to the joint measurement of more general pairs of observables are compared. They weaken the restrictions on “noisy” measurements that prevented the above method from being more generally usable, in two different ways: additive object-dependent noise versus object-independent non-additive noise. In the latter approach a lower bound for the amount of noise in a joint measurement of incompatible observables is found, not as a consequence of the usual Heisenberg scatter principle, but of a new “inaccuracy principle”. Physically realizable examples are given.

Uncertainty limits of the information exchange between a quantum system and an external meter

2021

It is not possible to obtain information about the observable properties of a quantum system without a physical interaction between the system and an external meter. This physical interaction is described by a unitary transformation of the joint quantum state of the system and the meter, which means that the information transfer from the system to the meter depends on the initial quantum coherence of the meter. In the present paper, we analyze the measurement interaction in terms of the changes of the meter state caused by the interaction with the system. The sensitivity of the meter can then be defined by evaluating the distinguishability of meter states for different values of the target observable. It is shown that the sensitivity of the meter requires quantum coherences in the generator observable that determines the magnitude of the back action of the meter on the system. The trade-off between measurement resolution and back action is decided by the relation between sensitivity...

Quantum cloning and distributed measurements

Physical Review A, 2001

We study measurements on various subsystems of the output of a universal 1 → 2 cloning machine, and establish a correspondence between these measurements at the output and effective measurements on the original input. We show that one can implement sharp effective measurement elements by measuring only two out of the three output systems. Additionally, certain complete sets of sharp measurements on the input can be realised by measurements on the two clones. Furthermore, we introduce a scheme that allows to restore the original input in one of the output bits, by using measurements and classical communication-a protocol that resembles teleportation.

Simplerealizations of generalized measurements in quantum mechanics

Foundations of Physics Letters, 1994

This paper discusses the approach to the analysis of measurements in quantum mechanics which is based on a set of "detection operators" forming a resolution of identity. The expectation value of each of these operators furnishes the counting rate at a detector for any object state that is prepared. "Predictable measurements" are those for which there is a representation in which only one element of each diagonal matrix representing each operator is not zero. A set of commuting detection operators defines the class of "spectral measurements", which may be either predictable or not. An even more general definition of measurement may be given by abandoning the requirement of commutativity of the detection operators. In this case one cannot define an observable which corresponds to a single self-adjoint operator, which violates the standard theory of quantum mechanical measurement.

“No Information Without Disturbance”: Quantum Limitations of Measurement

Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle (eds. W.C. Myrvold, J. Christian), pp. 229-256, 2009

In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise the notion that quantum measurements necessarily alter the system under investigation and elucidate its connection with the complementarity and uncertainty principles.

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 .