Quantum Measurement Process Research Articles

Non-Boolean probabilities and quantum measurement

A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum mechanical Hilbert space formalism and exhibits a particular phenomenon (state-independent conditional probabilities) which may provide new opportunities for an understanding of the quantum measurement process. Examples of the proposed model are provided, using Jordan operator algebras.

Quantum-state engineering with Josephson-junction devices

We review recent theoretical and experimental progress in quantum state engineering with Josephson junction devices. The concepts of quantum computing have stimulated an increased activity in the field. Either charges or phases (fluxes) of the Josephson systems can be used as quantum degrees of freedom, and their quantum state can be manipulated coherently by voltage and current pulses. They thus can serve as qubits, and quantum logic gates can be performed. Their phase coherence time, which is limited, e.g., by the electromagnetic fluctuations in the control circuit, is long enough to allow a series of these manipulations. The quantum measurement process performed by a single-electron transistor, a SQUID, or further nanoelectronic devices is analyzed in detail.

Reading-out the state of a qubit: an analysis of the quantum measurement process

Quantum measurements have to be performed in order to read out the final state of qubits in quantum computers. For a Josephson charge qubit [Phys. Rev. Lett. 79 (1997) 2371; Nature 386 (1999) 305] this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. As long as no transport voltage is applied to the SET, no dissipative currents flow, and the presence of the SET merely renormalizes (weakly) the parameters of the qubit. To perform a measurement, the transport voltage is turned on. The measurement process makes use of the high sensitivity of the current through the SET (the meter) to the voltage applied to the middle island. Since different states of the qubit differ in charge, the voltage felt by the SET, and the macroscopic, measurable current through it, depend on the state of the qubit.

Quantum coherence and entanglement

We are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects. Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it. In this special issue of Journal of Optics B: Quantum and Semiclassical Optics, we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.

Quantum measurement via Born-Oppenheimer adiabatic dynamics

The Born-Oppenheimer adiabatic approximation is used to describe the dynamic realization of wave-function collapse in quantum measurement. In the adiabatic limit, it is shown that the wave function of the total system formed by the measured quantum system plus the measuring apparatus can be factorized as an entangled state with correlation between adiabatic quantum states and quasiclassical motion configurations of the large system. When the apparatus effectively behaves as a classical object, this adiabatic entanglement leads to the wave-function collapse, which creates an ideal quantum measurement process.

Statistics and noise in a quantum measurement process

We study the quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum. This description applies for a wide class of quantum measurements.

Josephson junction quantum bits and logic gates

Low-capacitance Josephson junctions can serve as quantum bits, combining the coherence of the superconducting state with control mechanisms of single-charge systems. With logic states differing by one Cooper-pair charge, single- and two-bit gates can be performed by applying voltage and flux pulses. The phase coherence time is long enough to allow a series of these steps. In addition to the manipulations the resulting quantum state has to be read out, which can be accomplished by coupling the qubit to a single-electron transistor. To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. The system can be realized by present-day technology.

Quantum approach to coupling classical and quantum dynamics

We present a consistent framework of coupled classical and quantum dynamics. Our result allows us to overcome severe limitations of previous phenomenological approaches, like evolutions that do not preserve the positivity of quantum states or that allow to activate quantum nonlocality for superluminal signaling. A `hybrid' quantum-classical density is introduced and its evolution equation derived. The implications and applications of our result are numerous: it incorporates the back-reaction of quantum on classical variables, it resolves fundamental problems encountered in standard mean field theories, and remarkably, also the quantum measurement process, i.e. the most controversial example of quantum-classical interaction is consistently described within our approach, leading to a theory of dynamical collapse.

Quantum Measurement and Stochastic Processes in Mesoscopic Conductors

In quantum measurement theory it is necessary to show how a quantum source conditions a classical stochastic record of measured results. We discuss mesoscopic conductance using quantum stochastic calculus to elucidate the quantum nature of the measurement taking place in these systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/ outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. We show an equivalence between the approach of BÜttiker and the Fermi quantum stochastic calculus for mesoscopic systems.

On Time Asymmetry and History in an Everett Quantum World

It is usually held that the standard collapse model of a quantum measurement process grounds a kind of fundamental time asymmetry. The question whether and how it should be possible to reconstruct uniquely one's own history in an Everett no-collapse interpretation of quantum theory is investigated. A particular approach to the Everett interpretation, due to John S. Bell, is considered, according to which one of the chief claims of the Everett quantum theory is precisely that it allows us to do without the notion of history.

Complete Characterization of Arbitrary Quantum Measurement Processes

We examine two simple and feasible practical schemes allowing the complete determination of any quantum measuring arrangement. This is illustrated with the example of parity measurement.Received 22 December 1998DOI:https://doi.org/10.1103/PhysRevLett.83.3573©1999 American Physical Society

Information transmission in quantum measurement processes with pure operation

Quantum and classical informations are considered in quantum measurement processes described by pure operations. The quantum information is given by coherent information in the state change of the measured physical system, and the classical information represented by the Shannon mutual information is obtained from the measurement outcomes. It is shown that if the maximum classical information is obtained, the quantum information becomes zero and if any classical information is not obtained, all the quantum information that the physical system has can be transmitted.

State reduction, information and entropy in quantum measurement processes

Information obtained by a quantum measurement process performed on a physical system and the entropy change of the measured physical system are considered in detail. It is shown that the condition for the amount of information obtained by the quantum measurement process to be represented by the Shannon mutual entropy is that the intrinsic observable of the measured physical system commutes with the operational observable defined by the quantum measurement process. When some measurement outcome is obtained, the decrease of the Shannon entropy of the measured system is compared with that of the von Neumann entropy. Furthermore, a condition is established under which the amount of information that can be established by the quantum measurement process becomes equal to the decrease of the Shannon entropy of the measured physical system.

Partially reversible operation and information gain in quantum measurement processes

A partially reversible operation is introduced in quantum measurement processes and the information-theoretical property is investigated. The dual map of a partially reversible operation becomes reversible with respect to the intrinsic observable of a physical system. It is shown that the amount of information about the intrinsic observable of the physical system, obtained in a quantum measurement process described by a partially reversible operation, is equal to the decrease of the entropy of the measured physical system.

Quantum measurements performed with a single-electron transistor

Low-capacitance Josephson junction systems as well as coupled quantum dots, in a parameter range where single charges can be controlled, provide physical realizations of quantum bits, discussed in connection with quantum computing. The necessary manipulation of the quantum states can be controlled by applied gate voltages. In addition, the state of the system has to be read out. Here we suggest to measure the quantum state by coupling a single-electron transistor to the $q$-bit. As long as no transport voltage is applied, the transistor influences the quantum dynamics of the $q$-bit only weakly. We have analyzed the time evolution of the density matrix of the transistor and $q$-bit when a voltage is turned on. For values of the capacitances and temperatures which can be realized by modern nanotechniques, the process constitutes a quantum measurement process.

Information and Entropy in Quantum Measurement Processes

Quantum measurement processes of discrete andcontinuous observables are considered from theinformation-theoretic point of view. The informationextracted from the results of quantum measurementperformed on a physical system and the change of theShannon entropy of the measured physical system areinvestigated in detail. It is shown that the amount ofinformation about the intrinsic observable of themeasured physical system can be expressed by the mutualinformation between the physical system and themeasurement apparatus if the intrinsic observablecommutes with the operational observable defined by thequantum measurement process. Furthermore, the conditioncan be obtained under which the amount of informationextracted from the measurement outcomes becomes equal tothe decrease of the entropy of the measured physical system. In addition, the change of theShannon entropy is compared with that of the von Neumannentropy. The general results do not depend on whetherthe readout of the measurement outcome obeys the projection postulate or not. Severalexamples of quantum measurement processes are consideredto examine the general results.

‘Counterfactual’ interpretation of the quantum measurement process

The question of the determination of the state of the system during a measurement experiment is discussed within quantum theory, as a part of the more general measurement’s problem. I propose a counterfactual interpretation of the measurement process which answers the question from a conceptual point of view. This interpretation turns out to be consistent with the predictions of quantum theory, but it presents difficulties from an operational point of view.

Pure quantum states are fundamental, mixtures (composite states) are mathematical constructions: An argument using algorithmic information theory

From the philosophical viewpoint, two interpretations of the quantum measurement process are possible: According to the first interpretation, when we measure an observable, the measured system moves into one of the eigenstates of this observable (“the wave function collapses”); in other words, the universe “branches” by itself, due to the very measurement procedure, even if we do not use the result of the measurement. According to the second interpretation, the system simply moves into amixture of eigenstates, and the actual “branching” occurs only when anobserver reads the measurement results. According to the first interpretation, a mixture is a purely mathematical construction, and in the real physical world, a mixture actually means that the system is in one of the “component” states. In this paper, we analyze this difference from the viewpoint ofalgorithmic information theory; as a result of this analysis, we argue that onlypure quantum states are fundamental, while mixtures are simply useful mathematical constructions.

On dissipative stochastic equations in a Hilbert space

A general existence and uniqueness theorem for solutions of linear dissipative stochastic differential equation in a Hilbert space is proved. The dual equation is introduced and the duality relation is established. Proofs take inspirations from quantum stochastic calculus, however without using it. Solutions of both equations provide classical stochastic representation for a quantum dynamical semigroup, describing quantum Markovian evolution. The problem of the mean-square norm conservation, closely related to the unitality (non-explosion) of the quantum dynamical semigroup, is considered and a hyperdissipativity condition, ensuring such conservation, is discussed. Comments are given on the existence of solutions of a nonlinear stochastic differential equation, introduced and discussed recently in physical literature in connection with continuous quantum measurement processes.