Quantum retrodiction in open systems

Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum mechanics. Recent interest in quantum communications and cryptography, however, has provided retrodiction with a potential practical application. For this purpose quantum retrodiction in open systems should be more relevant than in closed systems isolated from the environment. In this paper we study retrodiction in open systems and develop a general master equation for the backward time evolution of the measured state, which can be used for calculating preparation probabilities. We solve the master equation, by way of example, for the driven two-level atom coupled to the electromagnetic field.Comment: 12 pages, no figure

Ultrahigh Error Threshold for Surface Codes with Biased Noise

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is in fact at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.Comment: 6 pages, 5 figures, comments welcome; v2 includes minor improvements to the numerical results, additional references, and an extended discussion; v3 published version (incorporating supplementary material into main body of paper

Detecting subsystem symmetry protected topological order via entanglement entropy

Subsystem symmetry protected topological (SSPT) order is a type of quantum order that is protected by symmetries acting on lower-dimensional subsystems of the entire system. In this paper, we show how SSPT order can be characterized and detected by a constant correction to the entanglement area law, similar to the topological entanglement entropy. Focusing on the paradigmatic two-dimensional cluster phase as an example, we use tensor network methods to give an analytic argument that almost all states in the phase exhibit the same correction to the area law, such that this correction may be used to reliably detect the SSPT order of the cluster phase. Based on this idea, we formulate a numerical method that uses tensor networks to extract this correction from ground-state wave functions. We use this method to study the fate of the SSPT order of the cluster state under various external fields and interactions, and find that the correction persists unless a phase transition is crossed, or the subsystem symmetry is explicitly broken. Surprisingly, these results uncover that the SSPT order of the cluster state persists beyond the cluster phase, thanks to a new type of subsystem time-reversal symmetry. Finally, we discuss the correction to the area law found in three-dimensional cluster states on different lattices, indicating rich behavior for general subsystem symmetriesComment: 17 pages. v2: Published version, minor changes throughou

The Role of Consumer Knowledge of Insurance Benefits in the Demand for Preventative Health

In 1992, the United States Centers for Medicare and Medicaid Services (CMS) introduced new insurance coverage for two preventive services influenza vaccinations and mammograms. Economists typically assume transactions occur with perfect information and foresight. As a test of the value of information, we estimate the effect of consumer knowledge of these benefits on their demand. Treating knowledge as endogenous in a two-part model of demand, we find that consumer knowledge has a substantial positive effect on the use of preventive services. Our findings suggest that strategies to educate the insured Medicare population about coverage of preventive services may have substantial social value.

Retrodictive states and two-photon quantum imaging

We use retrodictive quantum theory to analyse two-photon quantum imaging systems. The formalism is particularly suitable for calculating conditional probability distributions.Comment: 5 pages, 3 figure

Enhanced recovery after surgery

Enhanced Recovery or Fast Track Recovery after Surgery protocols (ERAS) have significantly changed perioperative care following colorectal surgery and are promoted as reducing the stress response to surgery. The present systematic review aimed to examine the impact on the magnitude of the systemic inflammatory response (SIR) for each ERAS component following colorectal surgery using objective markers such as C-reactive protein (CRP) and interleukin-6 (IL-6). A literature search was performed of the US National Library of Medicine (MEDLINE), EMBASE, PubMed, and the Cochrane Database of Systematic Reviews using appropriate keywords and subject headings to February 2015. Included studies had to assess the impact of the selected ERAS component on the SIR using either CRP or IL-6. Nineteen studies, including 1898 patients, were included. Fourteen studies (1246 patients) examined the impact of laparoscopic surgery on the postoperative markers of SIR. Ten of these studies (1040 patients) reported that laparoscopic surgery reduced postoperative CRP. One study (53 patients) reported reduced postoperative CRP using opioid-minimising analgesia. One study (142 patients) reported no change in postoperative CRP following preoperative carbohydrate loading. Two studies (108 patients) reported conflicting results with respect to the impact of goal-directed fluid therapy on postoperative IL-6. No studies examined the effect of other ERAS components, including mechanical bowel preparation, antibiotic prophylaxis, thromboprophylaxis, and avoidance of nasogastric tubes and peritoneal drains on markers of the postoperative SIR following colorectal surgery. The present systematic review shows that, with the exception of laparoscopic surgery, objective evidence of the effect of individual components of ERAS protocols in reducing the stress response following colorectal surgery is limited

Quantum State Tomography via Compressed Sensing

We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog^2d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed

A computationally universal phase of quantum matter

We provide the first example of a symmetry protected quantum phase that has universal computational power. Throughout this phase, which lives in spatial dimension two, the ground state is a universal resource for measurement based quantum computation.Comment: 5 + 2 page