Efficient Approximation of Quantum Channel Capacities

We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an $\varepsilon$-close estimate to the capacity, the presented algorithm requires $O(\tfrac{(N \vee M) M^3 \log(N)^{1/2}}{\varepsilon})$, where $N$ denotes the input alphabet size and $M$ the output dimension. We then generalize the method for the task of approximating the capacity of classical-quantum channels with a bounded continuous input alphabet and a finite dimensional output. For channels with a finite dimensional quantum mechanical input and output, the idea of a universal encoder allows us to approximate the Holevo capacity using the same method. In particular, we show that the problem of approximating the Holevo capacity can be reduced to a multidimensional integration problem. For families of quantum channels fulfilling a certain assumption we show that the complexity to derive an $\varepsilon$-close solution to the Holevo capacity is subexponential or even polynomial in the problem size. We provide several examples to illustrate the performance of the approximation scheme in practice.Comment: 36 pages, 1 figur

A Reasonable Captivity: Soldier Experiences in Camp Chase

Even compared to Libby Prison and Andersonville, one can recognize that conditions in Northern prisons like Camp Chase and Elmira Prison Camp were not ideal. Indeed, disease, death, and starvation were abundant in both Camp Chase and Elmira. However, they contrast greatly to the even more appalling conditions later in Libby and Andersonville. [excerpt

“The Scorpion’s Sting”: Dr. James Oakes and the 2014 Lincoln Lyceum Lecture

The annual Lincoln Lyceum Lecture took place on Thursday, March 27th at 7:30pm in Gettysburg College’s Mara Auditorium. This year’s Lincoln Lyceum guest speaker was Dr. James Oakes, two- time winner of the Lincoln Prize for his books The Radical and the Republican: Frederick Douglass (2008 Prize) and Abraham Lincoln and the Triumph of Antislavery Politics and Freedom National: The Destruction of Slavery in the United States, 1861 -1865 (2013 Prize). He has previously taught at Princeton University and Northwestern University and is currently the Distinguished Professor of History at the Graduate Center of the City University of New York. [excerpt

“A National Sin”: Samuel Simon Schmucker, Founder of Gettysburg College, on the Peculiar Institution

Many music and art students at Gettysburg College would recognize the name Schmucker as their building, or affectionately their ‘home,’ on campus. Alumni might even remember Schmucker Hall as their library. However, if asked who founded Gettysburg College, most students and alumni would probably not know his name. Fortunately, our campus is celebrating Founders Day this week to remember those, including our founder Samuel Simon Schmucker, who helped make our college #Gettysburgreat. [excerpt

Involving Others: Towards an Ethical Concept of Risk

Dr. Rehman-Sutter argues for a juridical concept of risk as it relates to an ethic of care. He also contrasts his view with traditional economic risk analysis

The Unfinished Work: The Civil War Centennial and the Civil Rights Movement

The Civil War Centennial celebrations fell short of a great opportunity in which Americans could reflect on the legacy of the Civil War through the racial crisis erupting in their nation. Different groups exploited the Centennial for their own purposes, but only the African Americans and civil rights activists tried to emphasize the importance of emancipation and slavery to the memory of the war. Southerners asserted states’ rights in resistance to what they saw as a black rebellion in their area. Northerners reflected back on the theme of reconciliation, prevalent in the seventy-fifth anniversary of the war. Unfortunately, those who had the most power to make an impact, government officials like the President and other Governors, tread lightly over the civil rights movement and instead focused on uniting a nation over anti-communism and Cold War sentiment. Fortunately, fifty years later, our nation has begun to recognize the real cause of the Civil War, but the “unfinished work” is not done

Love Amidst Tragedy: The Story of Sandie Pendleton and Kate Corbin

You might be having mixed feelings about this Valentine’s Day week: maybe you think love is wonderful, or perhaps you are more pessimistic about love and deem it impossible. Whatever the case, it was not entirely wonderful, nor quite impossible for soldiers during the Civil War. Love and war coexisted quite well, as you will read from other posts this week. Yet, as is the nature of both, they can also be tragic. Warning: the story I am about to tell you does not have a happy ending, but it is nonetheless heartwarming. [excerpt

Prisoner Experiences: Memoirs of Libby Prison

Numerous books have been written on the contested topic of Civil War prisons and prisoners of war. Scholars struggle with who to blame for the outrageous and horrible conditions of the prisons. Some speculate that the Southerners were crueler to their captives while others say the opposite. As well, scholars question whether the conditions of the Southern prisons were better or worse than the prisons in the North. [excerpt