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Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Apr. 02, 2016
Mar. 28, 2015
Apr. 02, 2016
Mar. 28, 2015
Jun. 27, 2015
Income Tax Disclosure [Abstract]          
(Benefit from) provision for income taxes $ 11.3 $ 4.8 $ 10.9 $ 19.1  
Valuation Allowance [Line Items]          
Unrecognized tax benefits 37.0   37.0   $ 37.4
Interest and penalties accrued 1.7   1.7    
Unrecognized tax benefits that may be recognized during the next twelve months 0.1   0.1    
Increase in Lumentum valuation allowance          
Valuation Allowance [Line Items]          
Onetime increase in valuation allowance immediately before the separation transaction     8.9    
Continuing operations          
Valuation Allowance [Line Items]          
Tax expense (benefit) from discontinued operations $ 7.6   $ (14.6)