"Zero Power" is usually a buzz-word / marketing term.
Zero power genuine occurs at zero current. This is not what you really want to know.
The IEC 62301 standard for measuring standby power in household electrical appliances rounds power usage of 5 mW or less to zero. So, 13 uA or less in your case - see below.
What matters depends on the source the energy and why you care.
325 VDC sounds like 230 VAC rectified - is that the source?
As a guide to costs - at 25 cents per unit, over a year (8765 hours) a Watt of power drawn continuously will cost you about $2.20. Adjust that figure for your power charges per unit.
1 Watt = P/V A = 1/375 = 2.7 milliamps
1 mW = 2.7 microamps
It is reasonably possible to achieve startup detection with ~= 3 mA available.
It's a lot harder with 3 uA.
One approach is storing energy in a capacitor with the detection circuit drawing extremely low current, with the capacitor giving an energy pool while waking up.
If uA level currents are needed and if sleep mode requires operation of an LED or similar then time multiplexing will be required to get useful drive levels. So 3uA with a 1:1000 duty cycle would allow a mA pulse once per second.
If you want more information please refine the question.
"The IEC 62301 standard for measuring standby power in household electrical appliances rounds power usage of 5 mW or less to zero."
iW1700 zero power controller IC
The iW1700 zero-power ac/dc digital PWM controller enables low-cost, energy-efficient 120/230V-ac offline adapters and chargers requiring as much as 5W, which consume zero no-load power for cell phones; audio players; digital cameras; and other lowpower, portable devices.
The device uses patented adaptive digital PWM/PFM technology that sends the controller into sleep mode when you disconnect the load, cutting no-load power consumption to less than 4 mW—effectively zero because the IEC 62301 standard for measuring standby power in household electrical appliances rounds power usage of 5 mW or less to zero.
Digital techniques enable the iW1700 to support primary-side control, eliminating the need for an optocoupler. It also features quasiresonant switching for low EMI, cycle-by-cycle waveform analysis, and a switching frequency as high as 72 kHz to achieve no-load charger performance, meet manufacturers’ power- supply requirements, and still enable a low BOM cost. The iW1700 comes in a low-cost, standard six-pin SOT-23 package and sells for 25 cents (10,000).
Good technical description
Acquired 2013 by: http://www.dialog-semiconductor.com/