Written by Bates Gill.

The enduring paradox of U.S.-China relations will be on full display this week in Washington in what will be one of the most important—and difficult—meetings between Presidents Barack Obama and Xi Jinping. Across so many dimensions of the relationship, the two countries have never been closer. Yet the underlying strategic foundation of the relationship—always fragile—has many new and troubling fissures.

On the one hand, the relationship continues a good-news story of deepening interdependence. For 2014, total bilateral goods trade reached $590 billion, making China the United States’ second-largest trading partner (just behind Canada), accounting for 15% of America’s total trade. China is America’s third-largest recipient of exports and is the largest exporter of goods to the United States—in 2014, nearly 17% of China’s exports went to American markets.

For the past several years, China has been the largest foreign holder of American treasury securities—contributing to lower borrowing rates in the United States and lessening appreciation of the Chinese renminbi against the U.S. dollar. As of July this year, China held $1.24 trillion in treasuries, or just over 20% of all foreign-held U.S. treasury securities, just ahead of Japan.

American majority-owned entities provided some 1.4 million jobs for Chinese workers in 2013. And Chinese-owned firms in the United States employed some 80,000 workers in America as of 2015, a more than eight-fold increase over 2007. In total, Chinese firms have invested about $46 billion in the United States since 2000, most of it in the past five years. Rhodium Group, a New York-based consultancy, predicts that figure could grow to between $100 and $200 billion by 2020.

The figures on people-to-people ties are even more remarkable. China is by far the single-largest source of foreign students attending educational institutions in America. In 2014 there were an estimated 274,000 Chinese students in America up from only 194,000 in 2012—a staggering 40% increase in just two years. Those 274,000 Chinese students make up 31% of the total number of foreign students in the States. Among these students in 2015 was a female Harvard undergraduate, Xi Mingze, who happens to be the only child of Xi Jinping. While America sends far fewer students annually to China—around 30,000—it is nevertheless the second-largest source of international students to China.

China will soon be the largest source of tourists traveling to America, with some 3 million such visitors predicted by 2019. Just over 2 million American tourists visited China in 2014, making them the third largest source of overseas visitors to China. This means skyrocketing air travel between the two countries. Between July and September this year, Chinese and U.S. airlines sent a total of 3,881 flights per week between the two countries according to CAPA Centre for Aviation, meaning every few minutes another flight is taking off in one direction or the other.

At an official level, the two sides have never been more deeply engaged, with some 90 regularized and ongoing bilateral dialogues on the full range of mutual concerns. And contrary to what one might think given the headlines, even U.S.-China military-to-military exchanges have steadily increased over time, and, as a result, the U.S. and Chinese militaries are today engaging at a level of seniority, frequency, and substance that is unprecedented, including high-level visits, recurrent exchanges, and joint multilateral and bilateral activities.

But, in the face of all these developments, a pervasive sense of distrust nevertheless underlies the strategic relationship between the two sides. Public moods in both countries are increasingly sour toward the other. Recent polling in the United States by the Pew Research Center shows that 54% of Americans have an unfavorable opinion toward China, marking a steady upward trend in that indicator over the past several years.

According to Pew polling this month, the list of principal American concerns about China include the large amount of American debt held by China, the loss of U.S. jobs to China, Chinese cyberattacks, Beijing’s poor human rights record, and China’s growing military power. Over 80% of Americans polled found these to be either “somewhat serious” or “very serious” problems.

Republicans in particular are tapping in to this angst—led by the party’s presidential contenders—and calling for tough measures in response. But no matter which party takes the White House next year, U.S. domestic politics will favor a harder line toward China. Even the U.S. business community, long-time staunch supporters of improved relations with China, has in recent years become less enamored, citing the increasing difficulties of doing business in China and a growing sense of being “unwelcome” there.

The public mood in China toward America is not much better. Since 2010, Chinese unfavorable views toward the United States have inched upward from 37% to as high as 53% in 2013 and 49% in the most recent Pew polling in 2015.

The comparatively newer challenges posed by cyberattacks and Chinese activities in the South China Sea add to a growing list of problems in the bilateral relationship. Overall, the Chinese side harbors deeply-held views that the United States is looking to “contain” China while undermining the legitimacy of the Chinese Communist Party. Americans are concerned about how China intends to exercise its power in the Asia-Pacific and what that will mean for American presence, allied relationships, and leadership in the region.

And beyond the bilateral relationship itself, the strategic atmosphere for both countries is fraught with tensions and uncertainties. In Europe, in Russia, and across the greater Middle East region, Washington is faced with growing challenges. The Chinese leadership, in spite of their country’s growing economic and military heft, nonetheless seems driven by apprehension, ratcheting up the security clampdown at home and flexing muscles around China’s periphery.

In this increasingly contentious atmosphere the two presidents will try to foster progress in the relationship.

Neither side will get everything it wants. Xi Jinping has telegraphed his expectation that the U.S. would respect China’s “core interests” and “avoid strategic misjudgment”. President Obama is unlikely to issue any strong words of support in acknowledgement of those concepts.

The U.S. side has signaled its intention to press the Chinese to halt their commercial cyberespionage and also commit to more constructive policies to clarify and resolve differences in the South and East China Seas in accordance with international norms. But Xi Jinping, constrained by domestic pressures to stand firm, is not likely to come at all close to what the U.S. side is looking for.

But for the summit to succeed, both sides will need to come away with some wins. As a result, expect incremental but valuable progress in two or three key areas where mutual interests are well-established.

It is clear both sides are committed to progressing the U.S.-China Bilateral Investment Treaty. It will not be finalized at this summit, but expect strong statements of commitment by both sides to get the treaty done.

Second, the two sides will likely announce new bilateral agreements to combat climate change and make a strong joint commitment to cooperatively negotiate substantive, legally binding outcomes with the other parties at the forthcoming United Nations Climate Conference in Paris at the end of this year. These announcements will build from the ambitious agenda of state and city-level actions put forward at the U.S.-China Climate Leaders summit held in California last week.

A third tantalizing possibility for agreement could arise in relation to cybersecurity. While garnering little attention, the visit of Meng Jianzhu, a Politburo member who heads the Commission for Political and Legal Affairs of the Party’s Central Committee, to Washington earlier this month holds some promise. He spent four days leading a cybersecurity delegation, meeting with U.S. officials including Secretary of State John Kerry, Secretary of Homeland Security Jeh Johnson and National Security Advisor Susan Rice.

Signals coming out of the White House, including from the President himself, underscore that cyber will be one of the “biggest topics” during the summit and suggest that Washington will urge Beijing to sign on to a basic “code of conduct” to restrain attacks against critical infrastructure during peacetime. Observers should definitely temper expectations at this stage, but finding and expanding any common ground on cybersecurity is a step in the right direction for U.S.-China relations.

So the paradoxical nature of U.S.-China relations—a complex mix of cooperation and contention—continues as it has for many decades, and the summit this week will be no different. That contentiousness has begun to weigh more heavily in the balance of late should compel statesmen on both sides to redouble efforts to expand their common ground, even if only incrementally. That will not only be good for the United States and China. It will benefit the world as well.

Dr. Bates Gill is Chief Executive Officer and Professor of Politics with the United States Studies Centre at the University of Sydney. A career-long follower of U.S.-China relations, he was formerly the Director of the Stockholm International Peace Research Institute (SIPRI), the Freeman Chair in China Studies at the Center for Strategic and International Studies, and Senior Fellow in Foreign Policy Studies and inaugural director of the Center for Northeast Asian Policy Studies at the Brookings Institution. Image credit: CC by U.S. Embassy The Hague/Flickr.