Strongly Incompatible Quantum Devices

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.Comment: 27 pages (AMSart), 6 figure

Incompatibility of Observables as State-Independent Bound of Uncertainty Relations

For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here we explore one possible route towards this goal through Heisenberg's uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we quantify the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, but not on the quantum state. To justify our case, we focus on the incompatibility of spin systems. For an arbitrary setting of two or three linearly-independent Pauli-spin operators, the incompatibility is analytically solved, the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, the measure of incompatibility represents a versatile tool for applications such as testing entanglement of bipartite states, and EPR-steering criteria.Comment: Comments are welcom

Compatibility and pricing with indirect network effects: evidence from ATMs

Incompatibility in markets with indirect network effects can reduce consumers’ willingness to pay if they value “mix and match” combinations of complementary network components. For integrated firms selling complementary components, incompatibility should also strengthen the demand-side link between components. In this paper, we examine the effects of incompatibility using data from a classic market with indirect network effects: Automated Teller Machines (ATMs). Our sample covers a period during which higher ATM fees increased incompatibility between ATM cards and other banks’ ATM machines. We find that incompatibility led to lower willingness to pay for deposit accounts. We also find that incompatibility benefited firms with large ATM fleets.Automated tellers

Freedom, Foreknowledge, and Dependence: A Dialectical Intervention

Recently, several authors have utilized the notion of dependence to respond to the traditional argument for the incompatibility of freedom and divine foreknowledge. However, proponents of this response have not always been so clear in specifying where the incompatibility argument goes wrong, which has led to some unfounded objections to the response. We remedy this dialectical confusion by clarifying both the dependence response itself and its interaction with the standard incompatibility argument. Once these clarifications are made, it becomes clear both (1.) that the dependence response does not beg the question against the proponent of the incompatibility argument and (2.) that the dependence response advances the dialectic whether it is developed as a version of Ockhamism or as a version of multiple-pasts compatibilism

Comparing the degrees of incompatibility inherent in probabilistic physical theories

We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all observable pairs. This opens up a novel and flexible way of comparing probabilistic theories with respect to the nonclassical feature of incompatibility, raising many interesting questions, some of which will be answered here. We show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have if arbitrary pairs of observables are considered. If one adopts a more refined measure of the degree of incompatibility, for instance, by restricting the comparison to binary observables, it turns out that there are probabilistic theories whose inherent degree of incompatibility is greater than that of quantum mechanics.Comment: Minor corrections in version 2, several new results added in version 3. Version 4 contains more detail on some proofs and terminological improvement

Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs

Incompatibility in markets with indirect network effects can affect prices if consumers value "mix and match" combinations of complementary network components. In this paper, we examine the effects of incompatibility using data from a classic market with indirect network effects: Automated Teller Machines (ATMs). Our sample covers a period during which higher ATM fees increased incompatibility between ATM cards (which are bundled with deposit accounts) and other banks' ATM machines. A series of hedonic regressions suggests that incompatibility strengthens the relationship between deposit account pricing and own ATMs, and weakens the relationship between deposit account pricing and competitors' ATMs. The effects of incompatibility are stronger in areas with high population density, suggesting that high travel costs increase both the strength of network effects and the importance of incompatibility in ATM markets.