Initial states and decoherence of histories

We study decoherence properties of arbitrarily long histories constructed from a fixed projective partition of a finite dimensional Hilbert space. We show that decoherence of such histories for all initial states that are naturally induced by the projective partition implies decoherence for arbitrary initial states. In addition we generalize the simple necessary decoherence condition [Scherer et al., Phys. Lett. A (2004)] for such histories to the case of arbitrary coarse-graining.Comment: 10 page

A review of the decoherent histories approach to the arrival time problem in quantum theory

We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expressed in terms of a POVM in this case. We turn finally to the question of decoherence of the corresponding histories, and we show that this can be achieved for simple states in the case of a free particle, and for general states for a particle coupled to an environment.Comment: 10 pages. To appear in DICE 2010 conference proceeding

Education y Justicia: A Living History of the Latinx Experience in U.T Austin

Social policy in the United States has historically and systematically prevented Latinx students from attaining educational equity. The resistance to this inequality in Austin is located in institutional spaces, the creation of cultural spaces, and the reclamation of erased histories. This has lead to the need for the creation of cultural spaces and legislation that encourage the equity, power, and culture of the Latinx community. We are mapping these living histories of resistance to help form frameworks for rethinking educational social policy. In this case we used U.T. and the greater Austin area to explore the living histories of the struggle for educational justice in our city and propose frameworks for rethinking educational social policy.Mexican American Studie

Consistent probabilities in loop quantum cosmology

A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have demonstrated how this issue can be successfully addressed within the consistent histories approach to quantum theory for Wheeler-DeWitt-quantized cosmological models. In this work, we generalize that analysis to the exactly solvable loop quantization of a spatially flat, homogeneous and isotropic cosmology sourced with a massless, minimally coupled scalar field known as sLQC. We provide an explicit, rigorous and complete decoherent histories formulation for this model and compute the probabilities for the occurrence of a quantum bounce vs. a singularity. Using the scalar field as an emergent internal time, we show for generic states that the probability for a singularity to occur in this model is zero, and that of a bounce is unity, complementing earlier studies of the expectation values of the volume and matter density in this theory. We also show from the consistent histories point of view that all states in this model, whether quantum or classical, achieve arbitrarily large volume in the limit of infinite `past' or `future' scalar `time', in the sense that the wave function evaluated at any arbitrary fixed value of the volume vanishes in that limit. Finally, we briefly discuss certain misconceptions concerning the utility of the consistent histories approach in these models.Comment: 22 pages, 3 figures. Matches published versio

Somewhere in the Universe: Where is the Information Stored When Histories Decohere?

We investigate the idea that decoherence is connected with the storage of information about the decohering system somewhere in the universe. The known connection between decoherence of histories and the existence of records is extended from the case of pure initial states to mixed states. Records may still exist but are necessarily imperfect. We formulate an information-theoretic conjecture about decoherence due to an environment: the number of bits required to describe a set of decoherent histories is approximately equal to the number of bits of information thrown away to the environment in the coarse-graining process. This idea is verified in a simple model consisting of a particle coupled to an environment that can store only one bit of information. We explore the decoherence and information storage in the quantum Brownian motion model. It is shown that the variables that the environment naturally measures and stores information about are the Fourier components of the function $x(t)$ (describing the particle trajectory). The records storing the information about the Fourier modes are the positions and momenta of the environmental oscillators at the final time. Decoherence is possible even if there is only one oscillator in the environment. The information count of the histories and records in the environment add up according to our conjecture. These results give quantitative content to the idea that decoherence is related to ``information lost''.Comment: 48 pages, plain Tex. Second revisio

Deccoherent Histories and Measurement of Temporal Correlation Functions for Leggett-Garg Inequalities

We consider two protocols for the measurement of the temporal correlation functions of a dichotomic variable Q appearing in Leggett-Garg type inequalities. The protocols measure solely whether Q has the same or different sign at the ends of a given time interval. They are inspired, in part, by a decoherent histories analysis of the two-time histories of Q although the protocols are ultimately expressed in macrorealistic form independent of quantum theory. The first type involves an ancilla coupled to the system with two sequential CNOT gates, and the two-time histories of the system are determined in a single final time measurement of the ancilla. It is non-invasive for special choices of initial system states and partially invasive for more general choices. Modified Leggett-Garg type inequalities which accommodate the partial invasiveness are discussed. The quantum picture of the protocol shows that for certain choices of primary system initial state the protocol is undetectable with respect to final system state measurements, although it is still invasive at intermediate times. This invasiveness can be reduced with different choices of ancilla states and the protocol is then similar in flavour to a weak measurement. The second type of protocol is based on the fact that the behaviour of Q over a time interval can be determined from knowledge of the dynamics together with a measurement of certain initial (or final) data. Its quantum version corresponds to the known fact that when sets of histories are decoherent, their probabilities may be expressed in terms of a record projector, hence the two-time histories in which Q has the same or different sign can be determined by a single projective measurement. The resulting protocol resembles the decay-type protocol proposed by Huelga and collaborators (which is non-invasive but requires a stationarity assumption).Comment: 33 pages. Revised appendix on LG inequalities for partially invasive measurements. Accepted for publication in Physical Review