While Washington wants Beijing to be part of any future treaty, Moscow is calling for the inclusion of Paris and London.

With the two nuclear superpowers now free of the restrictions imposed by the New START treaty, some experts fear another arms race.

Each side's statements are designed to get something from the other side without conceding anything themselves.

Here are three recurring themes in the dialogue so far.

- China hides its hand -

China has dismissed the idea of joining talks on a new nuclear arms limitation treaty.

As one Western diplomat put it, Beijing prefers to be "deliberately vague" on how hard it is pushing to catch up with the two major nuclear powers.

China has around 600 nuclear warheads in all, far fewer than the approximately 1,700 currently deployed by the United States and Russia between them -- and fewer still than the total number of warheads the two nuclear giants have in their stocks.

But most observers agree that China has stepped up production of its nuclear warheads. According to US estimates, they could number 1,000 by 2030 and possibly even 1,500 by 2035.

Testifying before the US Senate's Armed Services Committee on Tuesday, retired admiral and former commander of US Strategic Command (Stratcom) Charles A. Richard advised raising estimates of Chinese capabilities above "whatever the intelligence community tells you".

"Double it or triple it and you will probably be closer to where we're actually gonna wind up," he said.

China's opacity on this question raises problems, said Ja Ian Chong, a politics specialist at the National University of Singapore.

"That limited transparency and secrecy create grounds for miscalculation," he told AFP.

"Some observers think Beijing has an incentive to obscure its true capabilities, which can both protect its nuclear arsenal and provide some advantage in preventing potential adversaries from developing countermeasures," he added.

Granted, China insists it keeps its nuclear capability at the minimum required for national security, said Chong.

But he added: "There is no way to independently verify that claim."

- No hotline in Beijing -

A year after the 1962 Cuban Missile Crisis brought Russia and the United States to the brink of war, the two countries installed a hotline so their leaders could reach each other quickly in the event of a similar emergency.

China does not share that history.

As Admiral Richard told the US Senate committee: "One thing that Russia and the United States learned through the Cold War was how you responsibly operate systems of this great destructive potential.

"China, we don't know if they have learned the same lessons."

One reason China is reluctant to join nuclear weapons limitations talks is that it is so far behind the other two major powers, said Georgia Cole, a researcher at the London-based international affairs think tank Chatham House.

Trump might well want them at the negotiating table, she said. "But that's not going to happen in the interim because China has said that they won't engage in formal nuclear arms control until they achieve parity with the US and Russia."

- Russia's gambit -

Russia's response to the US insistence over China is to make the same demand of Europe's nuclear powers and UN Security Council members, Britain and France.

Gennady Gatilov, Moscow's ambassador to the conference on disarmament in Geneva, said Russian participation depended on that of the UK and France, "who are military allies of the United States in NATO".

The two countries possess fewer than 500 nuclear warheads between them.

But Russia wants them counted in a single Western "basket" along with the US nuclear arsenal, said Heloise Fayet, a security specialist at the French Institute of International Relations (IFRI).

That would turn them into "bargaining chips for the two great powers", she pointed out.

"France has always rejected this principle."

- Talk about the risks -

In Washington, Rose Gottemoeller, former US chief negotiator for the New START treaty, insisted before the US Senate committee that Beijing had to participate in future nuclear talks.

She had got the impression recently that "they seem very interested in trying to figure out ways to begin a conversation with the United States about nuclear risks", she said.

So even if Beijing did not want to engage in arms control talks, there was still a conversation to be had about these risks.

"They have a much smaller arsenal than ours," she acknowledged.

"But things like missile-launch notifications... hotline arrangements... are valuable to begin a conversation about the necessity of controlling nuclear weapons at the negotiating table and not being so untransparent about what they're doing with their modernisation," she argued.

"That has to be the first and foremost objective: talking to them about what their intentions are."