I've found two versions, and both feature the same flesh tone implying both the sensuality/sexuality of "passion," and the humanity of a passionate exchange. And both feature the austere title in a white, uneven color that suggests to me clouds or fog... something unclear...vague. Given the content of the show, which covers every possible form of "passion," the murky quality of the lettering makes perfect sense. And, though I have not seen the show yet, it seems to match the simplicity of a John Doyle production, where the simplicity of the staging belies a complexity of thought and content. And that certainly matches what is arguably the most complex of the Sondheim canon.
Taken together, the photos in the logos tell much about the three main characters and their "passion." In the above photo, there is a topless woman, bare back toward us - naked, vulnerable and alone. Notice that she's looking off into the distance. Does she see someone? Or is she looking off to the past or the future? While her lack of clothing intimates a certain kind of "passion," knowing the show, I'm betting she's unclothed to reveal her vulnerabilities, not necessarily her sexiness. Fosca?
The second logo shows an even more traditional expectation of "passion," a pairing apparently undressed (at least he appears to be sans shirt) and laying in an intimate arrangement. It certainly suggests post-coital togetherness. But look closer. Neither looks particularly spent - no misty sweat, her make-up is flawless, particularly her lips. Neither looks very happy, either - no smile, no look of pleasure. And notice that her eyes are closed, her mouth drawn closed, not frowning, but utterly expressionless. A sexual relationship, the photo suggests, is not a guarantee of happiness... so much happiness... Clara and Giorgio?
I'd say this is the perfect set of logos. It represents what the show is really about, while satisfying the expectations of the uninitiated. What more can you ask of a logo?