Ferreting out the Fluffy Bunnies: Entanglement constrained by Generalized superselection rules

Entanglement is a resource central to quantum information (QI). In particular, entanglement shared between two distant parties allows them to do certain tasks that would otherwise be impossible. In this context, we study the effect on the available entanglement of physical restrictions on the local operations that can be performed by the two parties. We enforce these physical restrictions by generalized superselection rules (SSRs), which we define to be associated with a given group of physical transformations. Specifically the generalized SSR is that the local operations must be covariant with respect to that group. Then we operationally define the entanglement constrained by a SSR, and show that it may be far below that expected on the basis of a naive (or ``fluffy bunny'') calculation. We consider two examples. The first is a particle number SSR. Using this we show that for a two-mode BEC (with Alice owning mode $A$ and Bob mode $B$), the useful entanglement shared by Alice and Bob is identically zero. The second, a SSR associated with the symmetric group, is applicable to ensemble QI processing such as in liquid-NMR. We prove that even for an ensemble comprising many pairs of qubits, with each pair described by a pure Bell state, the entanglement per pair constrained by this SSR goes to zero for a large ensemble.Comment: 8 pages, proceedings paper for an invited talk at 16th International Conference on Laser Spectroscopy (2003

Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis

We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean square error (MSE) that decreases at best as a power law ~N^{-2} in the number of measurements N. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to \exp(-0.3 N). That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in N.Comment: 5 pages, 3 figures, 1 table. Published versio

Entanglement under restricted operations: Analogy to mixed-state entanglement

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.Comment: 10 pages, 2 figures; published versio

The simplest demonstrations of quantum nonlocality

We investigate the complexity cost of demonstrating the key types of nonclassical correlations-Bell inequality violation, Einstein, Podolsky, Rosen (EPR)-steering, and entanglement-with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known Clauser-Horne-Shimony-Holt test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require nonprojective measurements. The simplest EPR-steering test requires a choice of projective measurement for one agent and a single nonprojective measurement for the other, while the simplest entanglement test uses just a single nonprojective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular two-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment

Symbiotic modeling: Linguistic Anthropology and the promise of chiasmus

Reflexive observations and observations of reflexivity: such agendas are by now standard practice in anthropology. Dynamic feedback loops between self and other, cause and effect, represented and representamen may no longer seem surprising; but, in spite of our enhanced awareness, little deliberate attention is devoted to modeling or grounding such phenomena. Attending to both linguistic and extra-linguistic modalities of chiasmus (the X figure), a group of anthropologists has recently embraced this challenge. Applied to contemporary problems in linguistic anthropology, chiasmus functions to highlight and enhance relationships of interdependence or symbiosis between contraries, including anthropology’s four fields, the nature of human being and facets of being human

Removal of a single photon by adaptive absorption

We present a method to remove, using only linear optics, exactly one photon from a field-mode. This is achieved by putting the system in contact with an absorbing environment which is under continuous monitoring. A feedback mechanism then decouples the system from the environment as soon as the first photon is absorbed. We propose a possible scheme to implement this process and provide the theoretical tools to describe it

One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering

We analyze the security and feasibility of a protocol for Quantum Key Distribution (QKD), in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and Device-Independent QKD (DI-QKD), where neither does, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.Comment: v2 replaces the 3-page abstract posted as v1: our results are now given with all necessary details. v3: published versio

Dialogue Concerning Two Views on Quantum Coherence: Factist and Fictionist

A controversy that has arisen many times over in disparate contexts is whether quantum coherences between eigenstates of certain quantities are fact or fiction. We present a pedagogical introduction to the debate in the form of a hypothetical dialogue between proponents from each of the two camps: a factist and a fictionist. A resolution of the debate can be achieved, we argue, by recognizing that quantum states do not only contain information about the intrinsic properties of a system but about its extrinsic properties as well, that is, about its relation to other systems external to it. Specifically, the coherent quantum state of the factist is the appropriate description of the relation of the system to one reference frame, while the incoherent quantum state of the fictionist is the appropriate description of the relation of the system to another, uncorrelated, reference frame. The two views, we conclude, are alternative but equally valid paradigms of description.Comment: 14 pages, Contribution to the Int. J. of Quant. Info. issue dedicated to the memory of Asher Peres; v2 updated summary and critique of prior literatur