Overcoming a limitation of deterministic dense coding with a non-maximally entangled initial state

Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its Schmidt coefficients is sqrt(1/d)), then Alice can convey to Bob one of d^2 distinct messages. If |Psi> is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode d^2-1 messages. Encoding d^2-2 is possible; see, e.g., the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when |Psi> is not maximally entangled, the communications limit of d^2-2 messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of |Psi> is sufficiently close to sqrt(1/d). In this protocol, d^2-2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d^2-1)-th message is encoded via a (non-trace-preserving) quantum operation.Comment: 18 pages, published versio

Deterministic dense coding and entanglement entropy

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of non-maximally entangled qudits in pure state |S>. Our results include the following: (i) We prove that it is possible for a state |S> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d = 3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d + j messages, j = 2, ..., d-1; moreover, we show that the j=2 and j= d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |S> allows the sending of K messages and has the square roof of c as its largest Schmidt coefficient, we show that the inequality c <= d/K, established by Wu et al. [ Phys. Rev. A 73, 042311 (2006)], must actually take the form c < d/K if K = d+1, while our constructions of local unitaries show that equality can be realized if K = d+2 or K = 2d-1.Comment: 19 pages, 2 figures. Published versio

Social Movements and Standing in the American Gun Debate

Who gets to be heard is a fundamental question in any democracy, and access to the arenas of political debate is every bit as contested as the disputes about policy within. The legal system offers rules of “standing” to determine who can make claims in a courtroom. We think the concept of standing is useful in making sense of access to a range of other political arenas as well. Notably, having an identifiable interest in the outcome of a particular set of decisions, a stake in the outcome, doesn’t necessarily grant a claimant access to an audience. Social movements work to convert stake into standing, and to win access to social and political arenas for distinct constituencies and claimants. Their arguments for access often parallel the legal criteria for standing. We provide an overview of the legal rules of standing, which afford judges considerable discretion in deciding who gets a hearing. We show that the rules for standing in the public sphere faintly echo those about access to a courtroom, although they are even less transparent and less reliable. Individuals and actors make claims about stake, expertise, and status to gain access to audiences in public debates, but standing is virtually always contested, contingent, and bounded. Using recent developments in the American gun debate, we detail political struggles for standing, considering the claims that various actors make in order to gain an audience. We find that significant audiences grant standing based on the political stance, rather than other identifiable criteria, contributing to a divisive and partisan debate, and critical challenges for making wise policies

Misleading assertions, unjustified assumptions, and additional limitations of a study by Patone et al., described in the article "Risk of Myocarditis After Sequential Doses of COVID-19 Vaccine and SARS-CoV-2 Infection by Age and Sex"

We describe several shortcomings of a study by Patone et al, whose findings were recently published in the American Heart Association Journal Circulation, including the following: * The study's principal conclusion, as initially stated, begins "Overall, the risk of myocarditis is greater after SARS-CoV-2 infection than after COVID-19 vaccination ...." However, Patone et al never attempt to assess the incidence of myocarditis in their study population following SARS-CoV-2 infection. Rather, they make an untenable assumption that all infections occurring in their study population are associated with (reported) positive COVID-19 tests. Using publicly available data from the UK's ONS and NHS, we show that Patone et al's estimates, for the unvaccinated, of myocarditis incidence associated with infection are likely overestimated by a factor of at least 1.58. * The method Patone et al use to compute the incidence of myocarditis among the unvaccinated after a positive COVID test may overestimate risk. The authors assume, without justification, that unvaccinated persons hospitalized during the study period with positive-test-associated myocarditis would later choose to vaccinate with the same probability as unvaccinated persons who have had a positive COVID test. We present a plausibility argument that suggests a possible further exaggeration of myocarditis risk post infection by a factor of 1.5. * Patone et al fail to discuss important limitations of their study with respect to guiding public health recommendations. For instance, at most 0.18% of SARS-CoV-2 cases that contributed to the study's finding were Omicron-variant cases. Thus, the study's estimates of myocarditis risk following infection do not speak to the risk following Omicron infection, which is recognized to be milder than that of previous variants.Comment: New section added (Section 4), conclusion updated (Section 6), 12 pages, 8 figure