There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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.

Quantum Computation and Quantum Information

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

Quantal phase factors accompanying adiabatic changes

Quantum teleportation — the transmission and reconstruction over arbitrary distances of the state of a quantum system — is demonstrated experimentally. During teleportation, an initial photon which carries the polarization that is to be transferred and one of a pair of entangled photons are subjected to a measurement such that the second photon of the entangled pair acquires the polarization of the initial photon. This latter photon can be arbitrarily far away from the initial one. Quantum teleportation will be a critical ingredient for quantum computation networks.

/pdf/experimental-quantum-teleportation-1cqrxvlpex.pdf

Experimental quantum teleportation

Entangled quantum states are not separable, regardless of the spatial separation of their components This is a manifestation of an aspect of quantum mechanics known as quantum non-locality An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography

Entanglement of the orbital angular momentum states of photons

We report on a high-intensity source of polarization-entangled photon pairs with high momentum definition. Type-II noncollinear phase matching in parametric down conversion produces true entanglement: No part of the wave function must be discarded, in contrast to previous schemes. With two-photon fringe visibilities in excess of 97%, we demonstrated a violation of Bell's inequality by over 100 standard deviations in less than 5 min. The new source allowed ready preparation of all four of the EPR-Bell states.

http://people.bu.edu/alexserg/Entangled.pdf

New high-intensity source of polarization-entangled photon pairs.

It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two‐particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin‐correlation and multiparticle interferometry examples are given of suitable three‐ and four‐particle arrangements, both at the gedanken and at the real experiment level.

Bell’s theorem without inequalities

So far experimental confirmation of entanglement has been restricted to qubits, i.e. two-state quantum systems including recent realization of three- and four-qubit entanglements. Yet, an ever increasing body of theoretical work calls for entanglement in quantum system of higher dimensions. Here we report the first realization of multi-dimensional entanglement exploiting the orbital angular momentum of photons, which are states of the electromagnetic field with phase singularities (doughnut modes). The properties of such states could be of importance for the efforts in the field of quantum computation and quantum communication. For example, quantum cryptography with higher alphabets could enable one to increase the information flux through the communication channels.

https://arxiv.org/pdf/quant-ph/0104070.pdf

Anton Zeilinger

Papers

Experimental quantum teleportation

Entanglement of the orbital angular momentum states of photons

New high-intensity source of polarization-entangled photon pairs.

Bell’s theorem without inequalities

Entanglement of Orbital Angular Momentum States of Photons