Move references in docstrings

docs/articles.bib

@@ -1,15 +1,16 @@
 #File for all article, arxiv and other web references
+# To add a key, Lastname_year_abbreviatedtitle/firstletteroftitle
 
 #Last name begins with A
-@misc{AaronsonMaxMixed,
+@misc{Aaronson_2018_MaxMixed,
   author  = {Aaronson, Scott},
   title   = "Lecture 6: Mixed States",
   howpublished = {https://www.scottaaronson.com/qclec/6.pdf}
 
 }
 
 
-@misc{arunachalam2017quantum,
+@misc{Arunachalam_2017_QuantumHedging,
       title={Quantum hedging in two-round prover-verifier interactions}, 
       author={Arunachalam, Srinivasan and Molina, Abel and Russo, Vincent},
       year={2017},
@@ -21,7 +22,7 @@ @misc{arunachalam2017quantum
 
 
 #Last name begins with B
-@article{Bandyopadhyay_2014,
+@article{Bandyopadhyay_2014_Conclusive,
    title={Conclusive exclusion of quantum states},
    volume={89},
    ISSN={1094-1622},

docs/books.bib

@@ -1,4 +1,5 @@
 #File for all book references
+# To add a key, Lastname_year_abbreviatedtitle OR firstletteroftitle
 
 #Last name begins with A
 
@@ -34,6 +35,7 @@
 
 #Last name begins with O
 
+
 #Last name begins with P
 
 #Last name begins with Q
@@ -49,7 +51,7 @@
 #Last name begins with V
 
 #Last name begins with W
-@book{watrous_2018, 
+@book{Watrous_2018_TQI, 
 place={Cambridge}, 
 title={The Theory of Quantum Information}, 
 DOI={10.1017/9781316848142}, 

toqito/channel_metrics/completely_bounded_trace_norm.py

@@ -12,7 +12,7 @@ def completely_bounded_trace_norm(phi: np.ndarray) -> float:
     Find the completely bounded trace norm of a quantum channel.
 
     Also known as the completely bounded diamond norm of a quantum
-    channel (Section 3.3.2 of :cite:`watrous_2018`). The algorithm in p.11 of :cite:`watrous2012simpler` with
+    channel (Section 3.3.2 of :cite:`Watrous_2018_TQI`). The algorithm in p.11 of :cite:`watrous2012simpler` with
     implementation in QETLAB :cite:`QETLAB_link` is used.
 
 

toqito/channel_metrics/fidelity_of_separability.py

@@ -39,7 +39,7 @@ def fidelity_of_separability(
     extension exists, it cannot be assumed directly that the state is
     separable. This function approximites the fidelity of separability by
     maximizing over PPT channels & k-extendible entanglement breaking channels
-    i.e. an optimization problem over channels :cite:`watrous_2018` .
+    i.e. an optimization problem over channels :cite:`Watrous_2018_TQI` .
 
     The following expression (Equation (I4) from :cite:`Philip2023schrodinger` ) defines the
     constraints for approximating

toqito/channel_ops/apply_channel.py

@@ -12,7 +12,7 @@
 def apply_channel(mat: np.ndarray, phi_op: np.ndarray | list[list[np.ndarray]]) -> np.ndarray:
     r"""Apply a quantum channel to an operator.
 
-    (Section: Representations and Characterizations of Channels of :cite:`watrous_2018`).
+    (Section: Representations and Characterizations of Channels of :cite:`Watrous_2018_TQI`).
 
     Specifically, an application of the channel is defined as
 

toqito/channel_ops/dual_channel.py

@@ -12,7 +12,7 @@ def dual_channel(
 ) -> np.ndarray | list[list[np.ndarray]]:
     r"""Compute the dual of a map (quantum channel).
 
-    (Section: Representations and Characterizations of Channels of :cite:`watrous_2018`).
+    (Section: Representations and Characterizations of Channels of :cite:`Watrous_2018_TQI`).
 
     The map can be represented as a Choi matrix, with optional specification of input
     and output dimensions. If the input channel maps :math:`M_{r,c}` to :math:`M_{x,y}`

toqito/channel_ops/kraus_to_choi.py

@@ -9,7 +9,7 @@
 def kraus_to_choi(kraus_ops: list[list[np.ndarray]], sys: int = 2) -> np.ndarray:
     r"""Compute the Choi matrix of a list of Kraus operators.
 
-    (Section: Kraus Representations of :cite:`watrous_2018`).
+    (Section: Kraus Representations of :cite:`Watrous_2018_TQI`).
 
     The Choi matrix of the list of Kraus operators, :code:`kraus_ops`. The default convention is
     that the Choi matrix is the result of applying the map to the second subsystem of the

toqito/channel_ops/partial_channel.py

@@ -16,7 +16,7 @@ def partial_channel(
     sys: int = 2,
     dim: list[int] | np.ndarray = None,
 ) -> np.ndarray:
-    r"""Apply channel to a subsystem of an operator :cite:`watrous_2018`.
+    r"""Apply channel to a subsystem of an operator :cite:`Watrous_2018_TQI`.
 
     Applies the operator
 

toqito/channel_props/choi_rank.py

@@ -9,7 +9,7 @@
 def choi_rank(phi: np.ndarray | list[list[np.ndarray]]) -> int:
     r"""Calculate the rank of the Choi representation of a quantum channel.
 
-    (Section 2.2: Quantum Channels from :cite:`watrous_2018`).
+    (Section 2.2: Quantum Channels from :cite:`Watrous_2018_TQI`).
 
     Examples
     ==========

toqito/channel_props/is_completely_positive.py

@@ -15,7 +15,7 @@ def is_completely_positive(
 ) -> bool:
     r"""Determine whether the given channel is completely positive.
 
-    (Section: Linear Maps Of Square Operators from :cite:`watrous_2018`).
+    (Section: Linear Maps Of Square Operators from :cite:`Watrous_2018_TQI`).
 
     A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is *completely
     positive* if it holds that

toqito/channel_props/is_herm_preserving.py

@@ -14,7 +14,7 @@ def is_herm_preserving(
 ) -> bool:
     r"""Determine whether the given channel is Hermitian-preserving.
 
-    (Section: Linear Maps Of Square Operators from :cite:`watrous_2018`).
+    (Section: Linear Maps Of Square Operators from :cite:`Watrous_2018_TQI`).
 
     A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is
     *Hermitian-preserving* if it holds that

toqito/channel_props/is_positive.py

@@ -14,7 +14,7 @@ def is_positive(
 ) -> bool:
     r"""Determine whether the given channel is positive.
 
-    (Section: Linear Maps Of Square Operators from :cite:`watrous_2018`).
+    (Section: Linear Maps Of Square Operators from :cite:`Watrous_2018_TQI`).
 
     A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is *positive* if it
     holds that

toqito/channel_props/is_quantum_channel.py

@@ -15,7 +15,7 @@ def is_quantum_channel(
     r"""Determine whether the given input is a quantum channel.
 
     (Section 2.2.1: Definitions and Basic Notions Concerning Channels from
-    :cite:`watrous_2018`).
+    :cite:`Watrous_2018_TQI`).
 
     A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is a *quantum
     channel* for some choice of complex Euclidean spaces :math:`\mathcal{X}`

toqito/channel_props/is_trace_preserving.py

@@ -16,7 +16,7 @@ def is_trace_preserving(
     dim: list[int] | np.ndarray = None,
 ) -> bool:
     r"""
-    Determine whether the given channel is trace-preserving (Section: Linear Maps Of Square Operators from :cite:`watrous_2018`).
+    Determine whether the given channel is trace-preserving (Section: Linear Maps Of Square Operators from :cite:`Watrous_2018_TQI`).
 
     A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is
     *trace-preserving* if it holds that

toqito/channel_props/is_unital.py

@@ -15,7 +15,7 @@ def is_unital(
     dim: int | list[int] | np.ndarray = None,
 ) -> bool:
     r"""
-    Determine whether the given channel is unital (Chapter: Unital Channels And Majorization from :cite:`watrous_2018`).
+    Determine whether the given channel is unital (Chapter: Unital Channels And Majorization from :cite:`Watrous_2018_TQI`).
 
     A map :math:`\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)` is *unital* if it
     holds that

toqito/channel_props/is_unitary.py

@@ -11,7 +11,7 @@ def is_unitary(phi: np.ndarray | list[list[np.ndarray]]) -> bool:
     r"""Given a quantum channel, determine if it is unitary.
 
     (Section 2.2.1: Definitions and Basic Notions Concerning Channels from
-    :cite:`watrous_2018`).
+    :cite:`Watrous_2018_TQI`).
 
     Let :math:`\mathcal{X}` be a complex Euclidean space an let :math:`U \in U(\mathcal{X})` be a
     unitary operator. Then a unitary channel is defined as:

toqito/channels/dephasing.py

@@ -7,7 +7,7 @@
 def dephasing(dim: int, param_p: float = 0) -> np.ndarray:
     r"""Produce the partially dephasing channel.
 
-    (Section: The Completely Dephasing Channel from :cite:`watrous_2018`).
+    (Section: The Completely Dephasing Channel from :cite:`Watrous_2018_TQI`).
 
     The Choi matrix of the completely dephasing channel that acts on :code:`dim`-by-:code:`dim`
     matrices.

toqito/channels/depolarizing.py

@@ -8,7 +8,7 @@ def depolarizing(dim: int, param_p: float = 0) -> np.ndarray:
     r"""Produce the partially depolarizing channel.
 
     (Section: Replacement Channels and the Completely Depolarizing Channel from
-    :cite:`watrous_2018`).
+    :cite:`Watrous_2018_TQI`).
 
     The Choi matrix of the completely depolarizing channel :cite:`WikiDepo` that acts on
     :code:`dim`-by-:code:`dim` matrices.

toqito/matrix_ops/vec.py

@@ -4,7 +4,7 @@
 
 def vec(mat: np.ndarray) -> np.ndarray:
     r"""
-    Perform the vec operation on a matrix ( Section: The Operator-Vector Correspondence from :cite:`watrous_2018`).
+    Perform the vec operation on a matrix ( Section: The Operator-Vector Correspondence from :cite:`Watrous_2018_TQI`).
 
     Stacks the rows of the matrix on top of each other to
     obtain the "vec" representation of the matrix.

toqito/matrix_props/is_commuting.py

@@ -14,7 +14,7 @@ def is_commuting(mat_1: np.ndarray, mat_2: np.ndarray) -> bool:
         \left[X, Y\right] = XY - YX.
 
     It holds that :math:`\left[X,Y\right]=0` if and only if :math:`X` and
-    :math:`Y` commute (Section: Lie Brackets And Commutants from :cite:`watrous_2018`).
+    :math:`Y` commute (Section: Lie Brackets And Commutants from :cite:`Watrous_2018_TQI`).
 
     Examples
     ==========

toqito/nonlocal_games/quantum_hedging.py

@@ -11,7 +11,7 @@ class QuantumHedging:
     Calculate optimal winning probabilities for hedging scenarios.
 
     Calculate the maximal and minimal winning probabilities for quantum
-    hedging to occur in certain two-party scenarios :cite:`arunachalam2017quantum, Molina_2012`.
+    hedging to occur in certain two-party scenarios :cite:`Arunachalam_2017_QuantumHedging, Molina_2012`.
 
     Examples
     ==========

toqito/state_metrics/fidelity_of_separability.py

@@ -36,7 +36,7 @@ def fidelity_of_separability(
     (Positive Partial Transpose (PPT), symmetric extensions (k-extendibility
     ) :cite:`Hayden_2013` ) This function approximites the fidelity of separability by
     maximizing over PPT states & k-extendible states i.e. an optimization
-    problem over states :cite:`watrous_2018`.
+    problem over states :cite:`Watrous_2018_TQI`.
 
     The following expression (Equation (H2) from :cite:`Philip2023schrodinger` ) defines the
     constraints for approxiamting

toqito/state_opt/state_exclusion.py

@@ -46,7 +46,7 @@ def state_exclusion(
                 \end{aligned}
             \end{equation}
 
-    The conclusive state exclusion SDP is written explicitly in :cite:`Bandyopadhyay_2014`. The problem of conclusive
+    The conclusive state exclusion SDP is written explicitly in :cite:`Bandyopadhyay_2014_Conclusive`. The problem of conclusive
     state exclusion was also thought about under a different guise in :cite:`Pusey_2012`.
 
     Examples

toqito/state_props/is_ensemble.py

@@ -6,7 +6,7 @@
 
 def is_ensemble(states: list[np.ndarray]) -> bool:
     r"""
-    Determine if a set of states constitute an ensemble (Section: Ensemble Of Quantum States from cite:`watrous_2018`).
+    Determine if a set of states constitute an ensemble (Section: Ensemble Of Quantum States from cite:`Watrous_2018_TQI`).
 
     An ensemble of quantum states is defined by a function
 

toqito/state_props/von_neumann_entropy.py

@@ -6,7 +6,7 @@
 
 def von_neumann_entropy(rho: np.ndarray) -> float:
     r"""
-    Compute the von Neumann entropy of a density matrix :cite:`WikiUVonNeumann`, Section: "Definitions Of Quantum Entropic Functions" from :cite:`watrous_2018`).
+    Compute the von Neumann entropy of a density matrix :cite:`WikiUVonNeumann`, Section: "Definitions Of Quantum Entropic Functions" from :cite:`Watrous_2018_TQI`).
 
     Let :math:`P \in \text{Pos}(\mathcal{X})` be a positive semidefinite operator, for a complex
     Euclidean space :math:`\mathcal{X}`. Then one defines the *von Neumann entropy* as

toqito/states/max_mixed.py

@@ -6,7 +6,7 @@
 
 def max_mixed(dim: int, is_sparse: bool = False) -> [np.ndarray, sparse.dia_matrix]:
     r"""
-    Produce the maximally mixed state :cite:`AaronsonMaxMixed`.
+    Produce the maximally mixed state :cite:`Aaronson_2018_MaxMixed`.
 
     Produces the maximally mixed state on of :code:`dim` dimensions. The maximally mixed state is
     defined as