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

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

Quantum entanglement

Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

Meeting the Universe Halfway is an ambitious book with far-reaching implications for numerous fields in the natural sciences, social sciences, and humanities. In this volume, Karen Barad, theoretical physicist and feminist theorist, elaborates her theory of agential realism. Offering an account of the world as a whole rather than as composed of separate natural and social realms, agential realism is at once a new epistemology, ontology, and ethics. The starting point for Barad’s analysis is the philosophical framework of quantum physicist Niels Bohr. Barad extends and partially revises Bohr’s philosophical views in light of current scholarship in physics, science studies, and the philosophy of science as well as feminist, poststructuralist, and other critical social theories. In the process, she significantly reworks understandings of space, time, matter, causality, agency, subjectivity, and objectivity.

In an agential realist account, the world is made of entanglements of “social” and “natural” agencies, where the distinction between the two emerges out of specific intra-actions. Intra-activity is an inexhaustible dynamism that configures and reconfigures relations of space-time-matter. In explaining intra-activity, Barad reveals questions about how nature and culture interact and change over time to be fundamentally misguided. And she reframes understanding of the nature of scientific and political practices and their “interrelationship.” Thus she pays particular attention to the responsible practice of science, and she emphasizes changes in the understanding of political practices, critically reworking Judith Butler’s influential theory of performativity. Finally, Barad uses agential realism to produce a new interpretation of quantum physics, demonstrating that agential realism is more than a means of reflecting on science; it can be used to actually do science.

Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning

Entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbitrary quantum state |\ensuremath{\xi}〉 can be transmitted at some rate Q through a noisy channel \ensuremath{\chi} without degradation. We prove that an EPP involving one-way classical communication and acting on mixed state M^(\ensuremath{\chi}) (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel \ensuremath{\chi}) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts ${\mathit{D}}_{1}$(M) and ${\mathit{D}}_{2}$(M) that can be locally distilled from it by EPPs using one- and two-way classical communication, respectively, and give an exact expression for E(M) when M is Bell diagonal. While EPPs require classical communication, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way communication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way communication is available. We exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single-error-correcting quantum block code. We prove that iff a QECC results in high fidelity for the case of no error then the QECC can be recast into a form where the encoder is the matrix inverse of the decoder. \textcopyright{} 1996 The American Physical Society.

Mixed State Entanglement and Quantum Error Correction

A theorem of Bell, proving that certain predictions of quantum mechanics are inconsistent with the entire family of local hidden-variable theories, is generalized so as to apply to realizable experiments. A proposed extension of the experiment of Kocher and Commins, on the polarization correlation of a pair of optical photons, will provide a decisive test between quantum mechanics and local hidden-variable theories.

Proposed Experiment to Test Local Hidden Variable Theories.

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

Two interferometric complementarities.

As Schrodinger discovered, the general principles of quantum mechanics imply that a quantum state of a many-particle system may be “entangled”, in the sense of not being a product of single-particle states. The concept of entanglement enters some deep investigations of the foundations of quantum mechanics, including the argument of Einstein-Podolsky-Rosen and the theorem of Bell. It is basic to the program of two-particle (or n-particle) interferometry. Of course, entanglement is exhibited by almost all of the interesting quantum states of atoms, molecules, nuclei, and condensed matter systems. The present report exhibits some mathematical relations among three concepts associated with entanglement. The second section proposes a general quantitative definition of the degree of entanglement E ( + ) of any n-particle quantum state and when n = 2 evaluates E ( + ) . (Note that the same symbol + is used for the quantum state and for the normalized vector in a Hilbert space that represents this state.) The third section is restricted to the case of two particles, each associated with a two-dimensional Hilbert space, called “the two-by-two case”. In this case, it is possible to calculate the two-particle fringe visibility V,*(+) and also the quantity B(+), which is the maximum deviation achievable, when the state is +, from the limit allowed by one of Bell’s inequalities. It is shown that V12(+) and B(+) are monotonic increasing functions of E ( + ) .

Abner Shimony

Papers

Proposed Experiment to Test Local Hidden Variable Theories.

Bell’s theorem without inequalities

Two interferometric complementarities.

Degree of Entanglementa

Optimal distinction between two non-orthogonal quantum states