Preparation information and optimal decompositions for mixed quantum states

Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.Comment: 13 pages, latex, 2 postscript figure

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte

On kinematics and dynamics of independent pion emission

Multiparticle boson states, proposed recently for 'independently' emitted pions in heavy ion collisions, are reconsidered in standard second quantized formalism and shown to emerge from a simplistic chaotic current dynamics. Compact equations relate the density operator, the generating functional of multiparticle counts, and the correlator of the external current to each other. 'Bose-Einstein-condensation' is related to the external pulse. A quantum master equation is advocated for future Monte-Carlo simulations.Comment: 10 pages LaTeX, Sec.7 adde

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.

Optimal generalized quantum measurements for arbitrary spin systems

Positive operator valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2 J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal POVM for the N=2 case, a rigorous bound for N=3 and set up the analysis for arbitrary N.Comment: LateX, 12 page

Optimal quantum teleportation with an arbitrary pure state

We derive the maximum fidelity attainable for teleportation using a shared pair of d-level systems in an arbitrary pure state. This derivation provides a complete set of necessary and sufficient conditions for optimal teleportation protocols. We also discuss the information on the teleported particle which is revealed in course of the protocol using a non-maximally entangled state.Comment: 10 pages, REVTe

Hypersensitivity to Perturbations in the Quantum Baker's Map

We analyze a randomly perturbed quantum version of the baker's transformation, a prototype of an area-conserving chaotic map. By numerically simulating the perturbed evolution, we estimate the information needed to follow a perturbed Hilbert-space vector in time. We find that the Landauer erasure cost associated with this information grows very rapidly and becomes much larger than the maximum statistical entropy given by the logarithm of the dimension of Hilbert space. The quantum baker's map thus displays a hypersensitivity to perturbations that is analogous to behavior found earlier in the classical case. This hypersensitivity characterizes ``quantum chaos'' in a way that is directly relevant to statistical physics.Comment: 8 pages, LATEX, 3 Postscript figures appended as uuencoded fil

Decoherence of geometric phase gates

We consider the effects of certain forms of decoherence applied to both adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit we illustrate path-dependent sensitivity to anisotropic noise and for two qubits we quantify the loss of entanglement as a function of decoherence.Comment: 4 pages, 3 figure

Unknown Quantum States: The Quantum de Finetti Representation

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an ``unknown quantum state'' in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point.Comment: 30 pages, 2 figure

Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information Processing

We construct a local realistic hidden-variable model that describes the states and dynamics of bulk-ensemble NMR information processing up to about 12 nuclear spins. The existence of such a model rules out violation of any Bell inequality, temporal or otherwise, in present high-temperature, liquid-state NMR experiments. The model does not provide an efficient description in that the number of hidden variables grows exponentially with the number of nuclear spins.Comment: REVTEX, 7 page