As the Australian public rallies behind government efforts to manage a way through the coronavirus pandemic, the success in mitigation appears to be rebuilding our broken public square.

Week on week more Australians are endorsing the government approach, believing it has struck the right balance, with support crossing tired and polarising partisan lines.

In our qualitative work we have also picked up a sense of common purpose, reinforcing findings last week that the Australian public considers itself as happy as it was 12 months ago. For the first time in my two decades of watching political research we are using the term “we” to describe the government.

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This is the product of two mutually reinforcing changes to our body politic: the prime minister’s decision to involve state governments in the national cabinet and to actively engage with stakeholders. And because of this, better decisions are being made, creating a virtuous cycle of nonpartisan governance born of necessity.

From this something even more profound is emerging: after a decade of erosion, trust in public institutions appears to be on the rise. We first picked up a decline in trust in the early teens as climate change became weaponised, it deteriorated as parties dumped leaders, and tapped the global anti-establishment sentiment that led to Brexit and put Donald Trump into the White House.

Just as trust in the media has been growing in recent weeks, so too have our public institutions been reasserting their importance, as shown in this week’s Guardian Essential Report.

Parliaments at a national, state and local level have experienced double-digit increases in trust, as have business groups and unions. Even political parties have moved forward in rebuilding their broken levels of trust.

These changes speak to a pool of social capital that will support governments to make the necessary but wicked decision of when and how to lift the lockdown and reopen the economy. This will never be simple, but higher levels of public trust maximise the chances of charting the best course through.

This trust is now being tested with calls on the public to embrace tracing technology the government believes is necessary to underpin the relaxing of distancing measures.

The PM has rightly ruled out making such technology compulsory. Rather, to work it will require a degree of social licence under which the public trusts the government to apply a technology that, on face value, will impinge on privacy and personal freedom.

After decades of increasing state surveillance of our online activity, meshed with increasingly creepy commercial tracking in attempts to predict our needs and desires as consumers, the idea of opening a new sphere of our lives is a stretch.

It should be noted that the questions were framed around the best available information last week, which was that people would actually be tracked. But the technological response appears to be an iterative process and we now know the government does not intend to actually track the movements. That said, the findings are still instructive in what the public is prepared to accept.

Even when framed around a more intrusive technology, take-up rights are within the range the government says is required to make the technology viable. But there are significant concerns about tracking and the government handling of public information, while just a bare majority of respondents believe that the app would be effective anyway.

This lack of trust in government is hardly surprising. After all, this is the same government that has deployed technology to raid reporters’ homes, harangue welfare recipients and crash the census.

Now in a time of crisis and public goodwill the onus is on the government to repay this newfound trust with clear guidelines on the way the technology will be used.

This could start by showing how the technology will effectively slow or stop the spread of the virus and pointing to international examples of where the technology has actually delivered on its promise rather than just offering up a magic data-driven wand.

It could then ensure information collected is not used for purposes other than tracking the contacts, ensuring any identifying information is kept secure and that it is destroyed when it is no longer required. This would need to include explicit exemptions from existing government laws that require carriers to render metadata in the name of national security.

It would also include a clear and transparent process on how the technology will be decommissioned after the pandemic, rather than forming a beta model for future monitoring for security or commercial purposes. Endorsing, for instance, calls for a moratorium on the extension of facial recognition technology until appropriate human rights frameworks are put in place, as recommended by the Australian Human Rights Commission, would underline this commitment.

Finally, if the government were really serious about building social licence it could ensure the information is held at arms length through the sort of public interest trusts that I have previously argued could provide the long-term antidote to surveillance capitalism.

The ultimate test of any tracking technology will be the strength of the relationship between the public and the government. With mutual respect and trust this could become part of the reopening of Australia but, like all relationships, this should not be taken for granted.

• Join Peter Lewis and Katharine Murphy to discuss the results of the latest Guardian Essential Report in Australia at Home’s Political Geekfest at 1pm on Tuesday