Topic

Quantum hypothesis testing

8 records: 8 unsolved, 0 solved. Filter the catalog by this topic →

Single-copy identity testing of local Gibbs states
What is the minimax copy complexity of identity testing two unknown \(k\)-local Gibbs states using only measurements on individual copies?
Unsolved
Fixed-error parallel Stein lemma for quantum channels
Let \(\mathcal N,\mathcal M:\mathcal L(A)\to\mathcal L(B)\) be quantum channels on finite-dimensional systems.
Unsolved
Chernoff exponents under separable and LOCC tests across copies
Determine the optimal symmetric discrimination exponents for two faithful noncommuting states when measurements must be separable across copies or implemented by local operations and classical communication (LOCC) among the copies.
Unsolved
Parallel versus nested-adaptive superchannel discrimination
Can nested-adaptive strategies improve the Stein exponent for discriminating two finite-dimensional quantum superchannels?
Unsolved
Statistical strength of CGLMP measurements
For every \(d\geq3\), do the standard CGLMP Fourier–phase measurements maximize the relative-entropy statistical strength against local realism among all projective \(d\)-outcome measurements on the fixed state \(\lvert\Phi_d\rangle=d^{-1/2}\sum_{j=0}^{d-1}\lvert j,j\rangle\), when the setting distribution is also optimized?
Unsolved
Advantage of fully general superchannel-discrimination strategies
Can a fully general adaptive strategy attain a larger Stein exponent than every nested-adaptive strategy for discriminating two quantum superchannels?
Unsolved
Generalized Stein lemma for fully quantum channel resources
Let \(\mathcal N:\mathcal L(A)\to\mathcal L(B)\) be a finite-dimensional quantum channel.
Unsolved
Square-root remainder in generalized quantum equipartition
Let \(H\) be a \(d\)-dimensional Hilbert space.
Unsolved