ENTANGLEMENT GAME FOR MACBOOK MAC
c A typical capacity region of a MAC (solid line), together with an achievable pentagonal region for a fixed input distribution (dashed lines).
The random variables corresponding to the senders and the receiver are denoted by A, B, and Z, respectively. b Mathematical model of a MAC N, characterized by finite input alphabets A and B, an output alphabet Z, and a conditional probability distribution N( z∣ a, b) for a ∈ A, b ∈ B, z ∈ Z. At the same time, entanglement assistance can push the achievable information transmission rates of MACs beyond the classical limit, paving the way for harnessing entangled resources in hybrid classical-quantum information networks.Ī Realistic scenario of a multiple access channel (MAC), in which two cell phones send data to a cell tower.
Our findings imply that even for the arguably simplest network information-theoretic setting of a MAC, there is no general solution to the problem of efficiently determining its unassisted communication capabilities, highlighting the need for practical approximation algorithms. Finally, we prove in the unassisted communication setting that it is NP-hard to determine which rates can be achieved for a given MAC. We also show that it is generally undecidable to determine whether the maximal rate pair can be achieved for a MAC with finite-dimensional entanglement strategies. Second, we exhibit examples of channels for which an unbounded amount of entanglement is needed to achieve the maximal possible increase of the achievable rate region. We demonstrate this by constructing a family of classical MACs with surprisingly rich behavior: First, we show that entanglement shared between the senders can strictly increase the capacity region of a classical MAC, proving that entanglement can help in a purely classical communication scenario. Moreover, even unassisted classical MACs exhibit far more complex behavior than previously widely appreciated. In this work, we show that MACs behave in a fundamentally different way in the presence of entanglement assistance, in contrast to the single-sender-single-receiver scenario. However, certain tasks such as classical single-sender-single-receiver communication receive no advantage from entanglement assistance 6. In quantum information theory, communication tasks can be enhanced dramatically if the communicating parties are given access to quantum resources such as shared entanglement 4, 5. Faithful information transmission through a MAC is possible within its capacity region, which was characterized by Ahlswede 2 and Liao 3 in terms of a so-called single-letter formula, i.e., an entropic optimization problem of fixed bounded dimension that is in principle computable. In network communication settings, the simplest model is a multiple access channel (MAC), where two spatially separated senders aim to transmit individual messages to a single receiver. Add these to your TBR pile, and don't forget to check out the Good Housekeeping book club once you're done, for even more fantastic stories.Information theory is the mathematical theory of communication and signal processing pioneered by Shannon 1. Alongside the love stories that categorize the form, many of our favorite romances also feature exciting plot lines, BIPOC and LGBTQ+ love stories and lyrical language that keep us breathless right through the final page. The romance realm has a lot to offer beyond the bodice-rippers you may have seen hiding in your mom's bedside table or waiting for impulse buyers at the grocery store checkout counter. Many of these great reads are romance-plus-other, so they're perfect for people who think they aren't into the genre. Whether you salivate over historical romance that takes you back to fluttering hearts of yesteryear, paranormal romance that proves you don't need flesh and blood to get frisky, rom-coms that pair hilarious misadventure with the steamy stuff or sexy stories that are too spicy for public transit, we've got a romance book to fit the bill. With both can't miss classics (If you haven't read Pride and Prejudice, what are you waiting for?) and brand-new reads (here's looking at you, Isaac Fellman), there's a little something for everyone on our list. Light some candles, grab your favorite sweet treat, slip into something comfy and get ready to turn up the heat with some of our favorite romance novels of all time.