Erwin Schrödinger

Bio: Erwin Schrödinger is an academic researcher from Dublin Institute for Advanced Studies. The author has contributed to research in topics: Humanism & Theory of relativity. The author has an hindex of 45, co-authored 135 publications receiving 20937 citations. Previous affiliations of Erwin Schrödinger include University of Graz & University of Vienna.

Die gegenwärtige Situation in der Quantenmechanik

Abstract: § 71. Die Au]hebung der ,,Verschrdinkung". Das Ergebnis abhdingig vom Willen des Experimentators. W i r kehren wieder zum al lgemeinen Fal l der ,Ve r sch r~nkung" znrfick, ohne gerade den besonderen Fa i l eines ~{eBvorgangs im Ange zu haben, wie soeben. Die Erwar tungska ta loge zweier 1{6> per A und B sollen sich durch vorf ibergehende Wechse lwi rkung verschr~nkt haben. J e t z t sollen die K6rper wieder ge t renn t seth. ] )ann kann ich einen davon, e twa B, hernehmen und meine unter m a x i m a l gewordene Kenntn is yon ihm du tch ?¢Iessungen sukzessive zu einer max ima len erggnzen. Ich behaup te : sobald mi r das z u m erstenmal gelingt, und nicht eher, wird erstens die Verschrgnkung gerade gel6st sein und werde ich zweitens durch die Messungen an B u n t e r Ausnf i tzung der Kondi t ionalsa tze , die bestanden, max ima le Kermtnis such yon A erworben haben. D e n n erstens Meibt die Kem~tnis yore Gesarntsys tem framer maximal , well sie du t ch gu ie und genaue Messungen keinesfalls ve rdorben wird. Zwei tens: Kondi t ionalsgtze yon der F o r m ,,wenn an A . . . . . . dann an B . . . . . " , kann es n icht mehr geben, sobald wi t yon B einen Maximalka ta log erlangt haben. Denn der ist nieht bedingt und zu ibm kann f iberhaupt nichts auf B Bezfigliches mehr h inzut re ten . Dr i t t ens : Kond i t i ona l s i t z e in umgekehr t e r R ich tung (,,wenn an B . . . . . . dann an A . . . . . ") lassen sich in S~itze fiber A allein umwandeln , well j a alle Wahrsche in l ichke i ten ffir B schon bedingungslos bekann t sind. Die Ver sch r in kung ist a lso rest los beseit igt , und da die Kenntn is v o m Gesamtsys t em max ima l gebl ieben ist, kann sie nur dar in bestehen, dab zum Maximalka ta tog ffir B ein ebensolcher ffir A h inzut r i t t . Es kann abe t such nicht e twa vorkommen, dab A indirekt , durch die Messungen an B, schon max ima l bekann t wird, bevor B es noch ist. Denn dann funkt ionieren alle Schlfisse in umgekehr t e r Richtung, d. h. B ist es au th . Die Sys teme werden gleichzeit ig max ima l bekannt , wie behaupte t . Nebenbei bemerkt , wfirde das such geiten, wenn man das Messen nicht gerade auf eines der beiden Sys teme beschrltnkt. Abe t das In teressante ist gerade, dab m a n es auf eines der beiden beschrgnken lcann; dab mari dami t ans ZieI kommt . Welche 5{essungen an B und in welcher iReihenfolge sie vo rgenommen werden, fat ganz der ~Nill-

Discussion of Probability Relations between Separated Systems

Abstract: The probability relations which can occur between two separated physical systems are discussed, on the assumption that their state is known by a representative in common. The two families of observables, relating to the first and to the second system respectively, are linked by at least one match between two definite members, one of either family. The word match is short for stating that the values of the two observables in question determine each other uniquely and therefore (since the actual labelling is irrelevant) can be taken to be equal. In general there is but one match, but there can be more. If, in addition to the first match, there is a second one between canonical conjugates of the first mates, then there are infinitely many matches, every function of the first canonical pair matching with the same function of the second canonical pair. Thus there is a complete one-to-one correspondence between those two branches (of the two families of observables) which relate to the two degrees of freedom in question. If there are no others, the one-to-one correspondence persists as time advances, but the observables of the first system (say) change their mates in the way that the latter, i.e. the observables of the second system, undergo a certain continuous contact-transformation.

What is life? : the physical aspect of the living cell ; Mind and matter

Abstract: Preface 1. The classical physicist's approach to the subject 2. The hereditary mechanism 3. Mutations 4. The quantum-mechanical evidence 5. Delbruck's model discussed and tested 6. Order, disorder and entropy 7. Is life based on the laws of physics? Epilogue: on determinism and free will Mind and Matter: 1. The physical basis of consciousness 2. The future of understanding 3. The principle of objectivation 4. The arithmetical paradox: the oneness of mind 5. Science and religion 6. The mystery of the sensual qualities Autobiographical sketches (translated from the German by Schrodinger's granddaughter Verena).

Quantum Computation and Quantum Information

Abstract: Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Entanglement of Formation of an Arbitrary State of Two Qubits

Abstract: The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state $\ensuremath{\rho}$ is the minimum average entanglement of an ensemble of pure states that represents \ensuremath{\rho}. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.

Quantum entanglement

Abstract: All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory} But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding However, it appeared that this new resource is very complex and difficult to detect Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon A basic role of entanglement witnesses in detection of entanglement is emphasized

Commentary: The Materials Project: A materials genome approach to accelerating materials innovation

Abstract: Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorganic materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform ‘‘rapid-prototyping’’ of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design. © 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Coherent and incoherent states of the radiation field

Abstract: Methods are developed for discussing the photon statistics of arbitrary fields in fully quantum-mechanical terms. In order to keep the classical limit of quantum electrodynamics plainly in view, extensive use is made of the coherent states of the field. These states, which reduce the field correlation functions to factorized forms, are shown to offer a convenient basis for the description of fields of all types. Although they are not orthogonal to one another, the coherent states form a complete set. It is shown that any quantum state of the field may be expanded in terms of them in a unique way. Expansions are also developed for arbitrary operators in terms of products of the coherent state vectors. These expansions are discussed as a general method of representing the density operator for the field. A particular form is exhibited for the density operator which makes it possible to carry out many quantum-mechanical calculations by methods resembling those of classical theory. This representation permits clear insights into the essential distinction between the quantum and classical descriptions of the field. It leads, in addition, to a simple formulation of a superposition law for photon fields. Detailed discussions are given of the incoherent fields which are generated by superposing the outputs of many stationary sources. These fields are all shown to have intimately related properties, some of which have been known for the particular case of blackbody radiation.