The Importance of Being Mathematical

839 0

Yes, the title is a play on Oscar Wilde’s classic comedy, but the playwright (and screenwriter) on my mind as I wrote this is:

Tom Stoppard (born Tomáš Sträussler, 3 July 1937) is a Czech-born British playwright and screenwriter. Three of his screenplays that I really enjoyed: The Russia House (1990), Shakespeare in Love (1998) for which he won an Academy Award for Best Screenplay, and Indiana Jones and the Last Crusade (1999).

Like Montaigne, I believe that ascetic renunciation is not only bad for health, but also unnatural and ungrateful (even ungodly ☺️). I am in New York – savoring nice wine, food and company (enjoyed lunch at Pera with Nihat Altintas, my PhD student now working on Wall Street, where I accidentally bumped into AJ Brohinsky, from SmartOps days, now in Private Equity, before stopping by at the new offices of QuantBot Technologies, a Hedge Fund Manager, you get the drift😏, followed by drinks with Tom and Shrinath, both CMU alums, brainstorming the next quantum (inspired) project to engage in, following up on our previous one, Alpha Optimal Combination (AOC) problem 😏, at the nearby rooftop bar Bookmarks) – just enjoying life.

I could not resist Broadway (O Broadway, Where Art Thou and Music Man) – and decided to see Leopoldstadt (instead of Some Like It Hot):

The Spectator: History will record Leopoldstadt as Tom Stoppard’s Schindler’s List.

The Telegraph: So here it is. Tom Stoppard’s last play. Very possibly. Britain’s greatest living dramatist has said that Leopoldstadt is likely to be the end of the road.

(Two important characters in the play are mathematicians, of different generations. They are part of the family portrayed, who are all just enjoying life, in fin de siècle Vienna, when the play begins. Tough topic, obviously, but quite well produced and acted, especially by the kids.😳 I wonder if this type of immersion is emotionally and mentally safe for them.)

You know that I love Matching Mathematics with Applications: indeed this is a delightful essence of my professional research career. Here is our new paper (joining the earlier ones as part of my Quantum Operations Research theme) that utilizes Markov Decision Process (MDP) to computationally study the optimal policy for using Entanglement Distillation in a Quantum Switch with the goal of maximizing its throughput with a constraint that any Entanglement Swap (yes, we are talking about engineering to accomplish quantum teleportation for secure quantum communication) should be above a fidelity threshold,

Optimal Entanglement Distillation Policies for Quantum Switches:

In an entanglement distribution network, the function of a quantum switch is to generate elementary entanglement with its clients followed by entanglement swapping to distribute end-to-end entanglement of sufficiently high fidelity between clients. The threshold on entanglement fidelity is any quality-of-service requirement specified by the clients as dictated by the application they run on the network. We consider a discrete-time model for a quantum switch that attempts generation of fresh elementary entanglement with clients in each time step in the form of maximally entangled qubit pairs, or Bell pairs, which succeed probabilistically; the successfully generated Bell pairs are stored in noisy quantum memories until they can be swapped. We focus on establishing the value of entanglement distillation of the stored Bell pairs prior to entanglement swapping in presence of their inevitable aging, i.e., decoherence: For a simple instance of a switch with two clients, exponential decay of entanglement fidelity, and a well-known probabilistic but heralded two-to-one distillation protocol, given a threshold end-to-end entanglement fidelity, we use the Markov Decision Processes framework to identify the optimal action policy – to wait, to distill, or to swap that maximizes throughput. We compare the switch’s performance under the optimal distillation-enabled policy with that excluding distillation. Simulations of the two policies demonstrate the improvements that are possible in principle via optimal use of distillation with respect to average throughput, average fidelity, and jitter of end-to-end entanglement, as functions of fidelity threshold. Our model thus helps capture the role of entanglement distillation in mitigating the effects of decoherence in a quantum switch in an entanglement distribution network, adding to the growing literature on quantum switches.

Back to Broadway. Will Tom Stoppard win his 5th Tony Award (on June 11th) where there are four CMU alums nominated (Jamie deRoy, as Producer of Leoploldstadt, which is one of her four nominations this year 😳, Christian Borle for Some Like It Hot, Nikki Crawford for Fat Ham and Josh Groban for Sweeney Todd)?

Leave a Reply