Revisiting Dynamics of Quantum Causal Structures-When Can Causal Order Evolve?

Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Castro-Ruiz et al. pursues this using the process-matrix formalism, together with a definition of the possible dynamics of such process matrices, and focusing especially on the question of evolution of causal structures. One of its major conclusions is a strong theorem saying that within the formalism, under continuous and reversible transformations, the causal order between operations must be preserved. Our result here challenges that of Castro-Ruiz et al.: if one is to take into account a full picture of the physical evolution of operations within the standard quantum-mechanical formalism, then the conclusion of Castro-Ruiz et al. does not hold. That is, we show that under certain continuous and reversible dynamics, the causal order between operations is not necessarily preserved. We moreover identify and analyse the root of this apparent contradiction, specifically, that the commonly accepted and widely applied framework of higher-order processes, whilst mathematically sound, is not always appropriate for drawing conclusions on physical dynamics. Finally, we show how to reconcile the elements of the whole picture following the intuition based on entanglement processing by local operations and classical communication.

Linear Program for Testing Nonclassicality and an Open-Source Implementation.

A well-motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex embeddability as introduced in Schmid et al. [PRX Quantum 2, 010331 (2021).2691-339910.1103/PRXQuantum.2.010331] and generalized in Selby et al. [Phys. Rev. A 107, 062203 (2023).PLRAAN2469-992610.1103/PhysRevA.107.062203].

Contextuality without Incompatibility.

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.

Uniqueness of Noncontextual Models for Stabilizer Subtheories.

We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross's discrete Wigner function. This representation is equivalent to Spekkens' epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross's representation by showing that (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality. Since negativity of this particular representation is a necessary resource for universal quantum computation in the state injection model, it follows that generalized contextuality is also a necessary resource for universal quantum computation in this model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions.

Oracles and Query Lower Bounds in Generalised Probabilistic Theories.

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), strong symmetry (existence of a rich set of nontrivial reversible transformations), and informationally consistent composition (roughly: the information capacity of a composite system is the sum of the capacities of its constituent subsystems). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, because fewer queries provide no information about the solution, then the corresponding "no-information" lower bound in theories lying at the kth level of Sorkin's hierarchy is ⌈ n / k ⌉ . This lower bound leaves open the possibility that quantum oracles are less powerful than general probabilistic oracles, although it is not known whether the lower bound is achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource that might have power beyond that offered by quantum computation.

A no-go theorem for theories that decohere to quantum mechanics.

To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification. Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both.

Entanglement is Necessary for Emergent Classicality in All Physical Theories.

One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance." These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.

Acute lower extremity compartment syndrome (ALECS) screening protocol in critically ill trauma patients.

BACKGROUND: Acute lower extremity compartment syndrome (ALECS) is a devastating complication that often presents silently in critically injured patients; therefore, we developed a protocol to screen high-risk patients. METHODS: This prospective observational study included all Shock Trauma intensive care unit patients who met specific high-risk criteria including pulmonary artery catheter-directed shock resuscitation, open or closed tibial shaft fracture, major vascular injury below the aortic bifurcation, abdominal compartment syndrome, or pelvic or lower extremity crush injury. Patients were screened at admission and every 4 hours thereafter for the first 48 hours of admission. Screening included physical examination (PE) and anterior or deep posterior calf compartment pressure measurements when PE was suspicious or unreliable. A positive screening, defined as a DeltaP <30 mm Hg (where DeltaP is the difference between the diastolic blood pressure and the compartment pressure), mandated a four-compartment fasciotomy. RESULTS: During a 6-month period, the incidence of ALECS in screened patients was surprisingly high at 20% (9 patients). With diligent screening, it was diagnosed early in the patient's Shock Trauma intensive care unit course. These were patients with severe injuries with an Injury Severity Score of 32.0 +/- 12.5 who exhibited significant volume depletion, with a base deficit of 12.9 +/- 5.9 mEq/L and a lactate level of 13.0 +/- 5.2 mmol/L, requiring large volume resuscitation. Although aggressive fasciotomy resulted in no limb loss, ALECS was associated with an exceedingly high mortality rate at 67%. CONCLUSIONS: ALECS is an important clinical entity in critically injured patients with trauma associated with significant mortality. Aggressive screening may provide some diagnostic insight to those at risk.

Preload optimization using "starling curve" generation during shock resuscitation: can it be done?

Preload-directed resuscitation is the standard of care in U.S. trauma centers. As part of our standardized protocol for traumatic shock resuscitation, patients who do not respond to initial interventions of hemoglobin replacement and fluid volume loading have optimal preload determined using a standardized algorithm to generate a "Starling curve." We retrospectively analyzed data from 147 consecutive resuscitation protocol patients during the 24 months ending August 2002. Fifty (34%) of these patients required preload optimization, of which the optimization algorithm was completed in 36 (72%). The average age of those who required preload optimization was 44 +/- 3 years vs. 34 +/- 1 years for patients who did not. Execution of the algorithm caused PCWP to increase from 18 +/- 1 mmHg to a maximum of 25 +/- 2 mmHg and CI to increase from 3.2 +/- 0.1 L/min m(-2) to 4.5 +/- 0.4 L/min m(-2). Algorithm logic determined PCWP = 24 +/- 2 to be optimal preload at the maximum CI = 4.8 +/- 0.4, and as the volume loading threshold for the remaining time of the resuscitation process. Starling curve preload optimization was begun 6.5 +/- 0.8 h after start of the resuscitation protocol and required 36 +/- 5 min and 4 +/- 0.4 fluid boluses (1.6 +/- 0.2 L). Comparison of early response of those patients who required preload optimization and those who did not indicated hemodynamic compromise apparent in the 1st 4 h of standardized resuscitation. We conclude that preload optimization using sequential fluid bolus and PCWP-CI measurement to generate a Starling curve is feasible during ICU shock resuscitation, but that there is the disadvantage that increasing and maintaining high PCWP may contribute to problematic tissue edema.