Completed in 2018, the project by David Chipperfield Architects transformed the cave from its former use as a Vicenza stone quarry.
The new photos by Sumner capture the imposing details of the former quarry, which is supported by giant piers deep beneath a wooded hill in the town of Zovencedo.
They also highlight David Chipperfield Architects' deliberately sensitive intervention, which is defined by steps intended to resemble stage sets by Swiss architect Adolphe Appia.
"Upon entering the caves, it is possible to experience space, material and structure as one unique entity, where nature and architecture seem to imitate each other," said David Chipperfield Architects.
"The romantic and tectonic qualities of the quarry with the carved stone and the filtered water were already so strong that minimal interventions were required."
Though Cava Arcari fell out of use in the 1950s, the transformation of Cava Arcari did not begin until 2010. It was the result of a collaboration between David Chipperfield Architects and Vicenza stone producer Laboratorio Morseletto.
Before this, Laboratorio Morseletto had been using the old quarry as a space for informal events but desired a more permanent performance venue.
The space is now defined by a series of steps, platforms and ramps formed from typical white Vicenza stone, intended as a continuation of the geology of the cave.
According to David Chipperfield Architects, these forms take cues from the works of Swiss architect and stage designer Appia as well as ancient Roman theatres.
Sumner said he was drawn to photographing Cava Arcari for the "visual traces of time" that can be seen throughout it.
"I'm intrigued by how architecture can leave visual traces of time, traces that a skilled eye can use to date a project," he told Dezeen.
"The photographer Simon Norfolk explored this idea in Kabul, dating building facades by the type and size of bullet holes," explained Sumner.
"Cava Arcari had a similar phenomenon – one could date different areas of the quarry by the marks left by the various mining technique used over the years."
In Sumner's photos, the stage lighting by the specialist company Viabizzuno is also revealed. Hidden in the corners of the cave, the light exaggerates the cavernous details and is reflected in deep pools of water throughout.
"The quarry had a series of long, deep flooded corridors, largely inaccessible," said Sumner. "They are also the final resting place of my sixth drone, having lost signal bouncing off a distant wall and sinking deep underwater."
David Chipperfield Architects was founded in 1985 by British architect David Chipperfield. It has offices in London, Berlin, Milan and Shanghai.
Renovations are a speciality of the studio, with its other overhauls including the revamp of Berlin's Neues Museum originally by Friedrich August Stüler and the Neue Nationalgalerie designed by Ludwig Mies van der Rohe.
The photography is by Edmund Sumner.