A Quantum-Bayesian Route to Quantum-State Space

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special attention paid to making all assumptions explici

Quantum copying: Fundamental inequalities

How well one can copy an arbitrary qubit? To answer this question we consider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal, then perfect copies can be made. If they are not, then errors will be introduced. The size of the error depends on the inner product of the two original vectors. We derive a lower bound for the amount of noise induced by quantum copying. We examine both copying transformations which produce one copy and transformations which produce many, and show that the quality of each copy decreases as the number of copies increases.Comment: 5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev.

Local Concurrent Error Detection and Correction in Data Structures Using Virtual Backpointers

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySDIO/IST managed by the Office of Naval Research / N00014-86-K-0519National Aeronautics and Space Administration / NASA NAG 1-602Joint Services Electronics Program / N00014-84-C-014

Application of Compiler-Assisted Multiple Instruction Rollback Recovery to Speculative Execution

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Aeronautics and Space Administration / NASA NAG 1-613Department of the Navy managed by the Office of the Chief of Naval Research / N00014-91-J-128

Phase covariant quantum cloning

We consider an N -> M quantum cloning transformation acting on pure two-level states lying on the equator of the Bloch sphere. An upper bound for its fidelity is presented, by establishing a connection between optimal phase covariant cloning and phase estimation. We give the explicit form of a cloning transformation that achieves the bound for the case N=1, M=2, and find a link between this case and optimal eavesdropping in the quantum cryptographic scheme BB84.Comment: 9 pages, 1 figur

Compiler-Assisted Multiple Instruction Rollback Recovery Using a Read Buffer

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Aeronautics and Space Administration / NASA NAG 1-613Department of the Navy / N00014-91-J-128

A toy model for quantum mechanics

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.Comment: in which the author breaks his vow to never use the words "ontic" and "epistemic" in publi

Fault-Tolerant Computing: An Overview

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNASA / NAG-1-613Semiconductor Research Corporation / 90-DP-109Joint Services Electronics Program / N00014-90-J-127

Information Invariance and Quantum Probabilities

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory.Comment: 8 pages, 1 figure. This article is dedicated to Pekka Lahti on the occasion of his 60th birthday. Found. Phys. (2009

Vortex Lattice Melting into Disentangled Liquid Followed by the 3D-2D Decoupling Transition in YBa_2Cu_4O_8 Single Crystals

A sharp resistance drop associated with vortex lattice melting was observed in high quality YBa_2Cu_4O_8 single crystals. The melting line is well described well by the anisotropic GL theory. Two thermally activated flux flow regions, which were separated by a crossover line B_cr=1406.5(1-T/T_c)/T (T_c=79.0 K, B_cr in T), were observed in the vortex liquid phase. Activation energy for each region was obtained and the corresponding dissipation mechanism was discussed. Our results suggest that the vortex lattice in YBa_2Cu_4O_8 single crystal melts into disentangled liquid, which then undergoes a 3D-2D decoupling transition.Comment: 5 pages, 4 eps figures, RevTex (Latex2.09