States
A quantum state is a density operator
where \(\mathcal{X}\) is a complex Euclidean space and where \(\text{D}(\cdot)\) represents the set of density matrices.
Distance Metrics for Quantum States
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Compute the fidelity of two density matrices [WikFid]. |
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Compute the Helstrom-Holevo distance between density matrices [WikHeHo]. |
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Compute the Hilbert-Schmidt distance between two states [WikHS]. |
Compute the Hilbert-Schmidt inner product between two matrices [WikHSO]. |
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Compute the sub fidelity of two density matrices [MPHUZSub08]. |
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Compute the trace distance between density operators rho and sigma. |
Compute the trace norm of the state [WikTn]. |
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Compute the Bures distance of two density matrices [WikBures]. |
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Compute the Matsumoto fidelity of two density matrices [Mat10]. |
Optimizations over Quantum States
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Compute probability of counterfeiting quantum money [MVW12]. |
Compute probability of optimally distinguishing a state via PPT measurements [COS13]. |
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Compute probability of state distinguishability [ELD03]. |
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Compute probability of single state exclusion. |
Helper functions for checking validity of states and probability vectors. |
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Compute optimal value of the symmetric extension hierarchy SDP [Nav08]. |
Operations on Quantum States
Convert a state vector or density matrix to a density matrix. |
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Compute the Schmidt decomposition of a bipartite vector [WikSD]. |
Properties of Quantum States
Calculate the concurrence of a bipartite state [WikCon]. |
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Compute entanglement-of-formation of a bipartite quantum state [WikEOF]. |
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Determine whether there exists a symmetric extension for a given quantum state. |
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Check whether an operator is contained in ball of separability [GB02]. |
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Determine if a set of states constitute an ensemble [WatEns18]. |
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Determine if a given quantum state is mixed [WikMix]. |
Check if list of vectors are mutually orthogonal [WikOrthog]. |
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Check if list of vectors constitute a mutually unbiased basis [WikMUB]. |
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Determine whether or not a matrix has positive partial transpose [WikPPT]. |
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Determine if a given vector is a product state [WikProdState]. |
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Determine if a given state is pure or list of states are pure [WikIsPure]. |
Compute the l1-norm of coherence of a quantum state [RPWL17]. |
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Compute the log-negativity of a bipartite quantum state [WikLogNeg]. |
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Compute the negativity of a bipartite quantum state [WikNeg]. |
Compute the purity of a quantum state [WikPurity]. |
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Compute the Schmidt rank [WikSR]. |
Check if state is separable. |
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Compute the von Neumann entropy of a density matrix [WikVent]. |
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Compute the S(k)-norm of a vector [NJDK09]. |
Quantum States
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Obtain the ket of dimension |
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Produce a Bell state [WikBell]. |
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Produce all Brauer states [WikBrauer]. |
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Produce a Breuer state [HPBreuer]. |
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Produce a chessboard state [BP00]. |
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Produce a generalized Bell state [DL09]. |
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Generate a (generalized) GHZ state [GHZ07]. |
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Produce a Gisin state [GIS96]. |
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Produce a isotropic state [HH99]. |
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Produce a maximally entangled bipartite pure state [WikEnt]. |
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Produce the maximally mixed state [AAR6]. |
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Produce a Tile state [UPBTile99]. |
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Produce a W-state [DVC00]. |
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Produce a Werner state [Wer89]. |
Produce a generalized singlet state acting on two n-dimensional systems [Gsinglet]. |