Tag: trace-distance

8 What is intuition for the trace distance between quantum states? 2019-07-11T03:11:22.173

7 Does the trace distance have a geometrical interpretation? 2019-11-07T13:02:55.623

6 Is the diamond norm subadditive under composition? 2019-08-17T13:38:41.133

6 Prove that $\|p^{\otimes n} - q^{\otimes n}\| \leq n \|p-q\|$ for density operators $p,q$ 2019-10-27T19:00:37.650

5 Prove that for one-qubit unitaries $\text{Tr}|U-V|=2\max_\psi\|(U-V)|\psi\rangle\|$ 2020-05-04T00:25:25.527

5 Closeness of purifications of states 2020-11-21T16:15:59.580

4 Is the quantum state fidelity defined as $F(\rho, \sigma)=\text{tr}\sqrt{\rho^{1/2}\sigma\rho^{1/2}}$ or its square? 2020-04-13T15:30:02.260

4 Is the trace distance between multipartite states invariant under permutations? 2020-11-26T01:30:53.983

4 Why do probablity distribution with orthogonal suppor have maximal Kolmogorov distance? 2021-01-28T10:25:13.030

3 Trace distance of two classical-quantum states 2019-05-16T16:03:28.727

3 Does the trace distance between marginals bound the distance between the overall states? 2020-05-13T22:13:10.513

3 Quantum marginal problem - constructing a global state from reduced states 2020-10-21T20:04:12.460

3 How can we upper bound the norm of a partial trace? 2020-11-23T21:08:01.107

2 It two unitaries are delta apart in trace norm, then what is the trace norm of outputs states when the same input state is applied to two unitaries? 2020-04-06T07:35:17.560

2 Continuity bounds on $D_{\max}(\rho_{AB}\|\rho_A\otimes\rho_B)$ 2020-04-12T00:06:15.013

2 What can be said about the closeness of two states if the difference of their fidelity measured with respect to a fixed state is close to 0? 2020-06-18T06:59:53.357

2 Saturating the Fuchs-van de Graaf inequality 2020-06-25T17:12:56.417

2 How do I prove that $\newcommand{\tr}{\operatorname{Tr}}\tr(A \sqrt{B} A \sqrt{B}) = \tr\Big[\Big(\sqrt{\sqrt{B}} A \sqrt{\sqrt{B}}\Big)^2\Big]$? 2020-10-16T16:34:19.893

2 Prove that the trace norm is dual to the spectral norm 2020-10-28T00:01:04.970

2 Properties of composition of isometry and a perturbed adjoint 2020-11-11T12:40:55.193

1 Can the fidelity $F(\rho,\sigma)$ be computed knowing only $\rho - \sigma$? 2020-07-03T02:06:30.460

1 Is the restriction of a strictly contractive channel (SCC) to a subspace necessarily still SCC? (impossibility of perfect QEC for SCCs) 2020-07-28T09:23:23.383

1 Relation between trace distance and inner product between pure states 2020-08-29T04:48:54.707

1 Relationship between trace distance and total variation distance 2020-09-01T03:23:45.780

1 Trace distance bound after partial trace 2020-10-27T06:27:43.080

1 Trace distance of two classical-quantum state with hashing 2020-11-05T07:45:21.747

0 Prove that $\operatorname{Tr}_B(O_A M)=O_A\operatorname{Tr}_B(M)$ 2020-04-24T20:40:25.863