LONDON, UK - Despite battling for nearly two hours to overcome Valentini Grammatikopoulou in the first round of Wimbledon qualifying last week 6-4, 3-6, 10-8, Kaja Juvan was in ebullient mood afterwards as she sat down - not least when best friend Iga Swiatek, who had been cheering her on, cheerfully gatecrashed an interview with that descended into banter and giggles as the two teenagers discussed their friendship and their shared "weirdness".

One week later, Juvan's career-best Grand Slam has taken her all the way into the second round: victory over Birmingham quarterfinalist Kristyna Pliskova, the Slovenian's first over a Top 100 player, has set up the biggest match of her life, a clash with 23-time major champion Serena Williams.

But the 18-year-old has plenty of experiences to draw on that should stand her in good stead - not least her debut on a Grand Slam show court last month at Roland Garros.

Juvan had lost a heartbreaker in the final round of qualifying to Bernarda Pera 6-4, 1-6, 7-6(1) - and to compound the gloom, had been drawn third in the lucky loser ballot, with only two spots open. "We waited the whole Saturday and Sunday and honestly, I thought I wasn't going to get in so I was a bit bummed," she recalls. "And then I warmed up with Johanna Konta, and during it - this was at about 10am [on Monday] - the WTA woman came and she was like, Kaja, are you ready? You're going to play instead of [Petra] Kvitova. And you're going to play on Suzanne Lenglen."

Having had a mere two hours to prepare for the first Grand Slam match of her career, Juvan - the singles and doubles gold medallist at last year's Youth Olympic Games in Buenos Aires - acquitted herself well but was edged out 5-7, 6-4, 7-5 by the experienced Sorana Cirstea. "My nerves got the best of me," she nods. "I really, really wanted to win and maybe that was the problem."

The Slovenian has learned quickly: at Wimbledon, she has come out on the winning side of three tough three-setters out of four matches. During qualifying, she was cheered on courtside by best friend Iga Swiatek, last year's Wimbledon junior champion and Juvan's Olympic partner.

The pair have been long-time junior comrades, having first met in Tennis Europe's Summer Cups competition in 2014, although it had not escaped Juvan's notice that the Pole's support was less than vociferous. "I saw you were reading!" she laughs as Swiatek lurks in the background. "Because I was watching you too during changeovers."

Swiatek justifies herself heartily. "Every time I looked at my book, you played better. That was a fact! Every time you had 40-15 or had match points, I started watching, and you lost them."

By now, Swiatek has joined in the interview, and the duo start to veer from their Olympic experience (Juvan: "In the doubles final, honestly, I was so tired, Iga carried me through - I just started pushing the ball in and she did everything else and then I collapsed in her arms at the end. And then I had also singles and both of my legs were falling off. It was really, really special") to Netflix (The Good Place is a shared favourite, although Juvan says she was hesitant to recommend it to Swiatek "because I thought she might not like the humour"). Bantering all the while, they make a strong case for one of the best up-and-coming buddy comedy pairs on the WTA Tour.

This is particularly the case when they begin teasing each other about their "weird" reading tastes. "If I want something to shut my brain off I read some sleazy romantic teenage books," says Juvan - but that's not where her heart really is. "But if I want to read something for pleasure, I read psychology, and I like philosophy as well."

Who are her favourite philosophers? "I like Socrates - it's really interesting because it was right at the beginning of philosophy - he started it. And then there's this saying from Descartes that faith is a projection of humanity, and I think that's a really smart saying because it's really related to God, and I think that's something humans like to do."

Swiatek interjects: "That's probably the only WTA interview where someone has mentioned Descartes." Juvan grins. "That's why I'm her friend, because we both have weird tastes!" Rolling her eyes for effect, Swiatek begins to distance herself - "I'm not that weird!" - but Juvan isn't having any of this claim to normality.

"Oh my God, you read about queens and kings of the 14th century!" Throwing her hands up, Swiatek admits defeat. "I like historical novels, OK? It's my thing." Reaching into her bag, she pulls out a Henry VIII T-shirt she has bought as a present for her coach, and the teenagers collapse into giggles.

When she's not pondering Cartesian dualism or the Socratic method, Juvan says she likes to relax by painting. Indeed, her last birthday present for Swiatek was a watercolour portrait - and although the self-deprecating teenager insists she "can't really paint", Swiatek disagrees emphatically and scrolls through her phone to show me how good Juvan's art is. (It is, indeed, impressive.) On court, too, Juvan is an artist: she describes her game style as "quite diverse", and her fondness for sharp angles and deft dropshots has been on full display over the past week.

What might make Juvan's breakthrough week even more impressive is that she had few expectations for herself ahead of it. Busy with her final year of high school, she hasn't even had enough time for her beloved philosophy. "I've been studying so much lately and I haven't been practising enough," she admitted. One week, four wins and a dream matchup later, it seems to have worked out well anyway for Juvan.