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Function over linear operators
analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar-valued function on operators, the partial trace is an operator-valued
Partial_trace
Sum of elements on the main diagonal
This trace can be generalized to von Neumann Algebras. The Dixmier trace generalizes the usual trace beyond trace-class operators. The partial trace is
Trace_(linear_algebra)
Principle in quantum information theory
over a subspace, it is technically called a partial trace. Key to this step is that the (partial) trace adequately summarizes the system from Bob's point
No-communication_theorem
Boundary condition for generalized functions
not exist and the trace operator T {\textstyle T} presented here must be used to give meaning to u | ∂ Ω {\textstyle u|_{\partial \Omega }} . Then u
Trace_operator
Derivative of a function with multiple variables
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held
Partial_derivative
Loss of quantum coherence
vanishing of the off-diagonal elements of the partial trace of the joint system's density matrix, i.e. the trace, with respect to any environmental basis,
Quantum_decoherence
Mathematical tool in quantum physics
\right|\right)\right],} where tr 2 {\displaystyle \operatorname {tr} _{2}} denotes the partial trace over the Hilbert space H 2 {\displaystyle {\mathcal {H}}_{2}} . This
Density_matrix
Process in linear algebra
the rank 1 matrix ρ = w w ∗ {\displaystyle \rho =ww^{*}} . Then the partial trace of ρ {\displaystyle \rho } , with respect to either system A or B, is
Schmidt_decomposition
Concept in quantum information theory
purification allows the original mixed state to be recovered by taking the partial trace over the additional degrees of freedom. The purification is not unique
Quantum_state_purification
Measure in quantum information theory
variables x or y. The corresponding operation for density matrices is the partial trace. So one can assign to ρ a state on the subsystem A by ρ A = Tr B ρ A
Quantum_mutual_information
Mathematical entity to describe the probability of each possible measurement on a system
state of the part H 1 {\displaystyle H_{1}} is expressed then as the partial trace over H 2 {\displaystyle H_{2}} . A mixed state cannot be described with
Quantum_state
Relationship of various quantum subsystems
2 {\displaystyle {\mathcal {H}}^{1}\otimes {\mathcal {H}}^{2}} as a partial trace: ρ 12 = T r H 3 ρ 123 {\displaystyle \rho ^{12}={\rm {Tr}}_{{\mathcal
Strong subadditivity of quantum entropy
Strong_subadditivity_of_quantum_entropy
National parkway in the southeastern U.S.
The Natchez Trace Parkway is a limited-access national parkway in the Southeastern United States that commemorates the historic Natchez Trace and preserves
Natchez_Trace_Parkway
Operation in mathematics
and contraction operations make sense in this context. Tensor product Partial trace Interior product Raising and lowering indices Musical isomorphism Ricci
Tensor_contraction
TAAR1 agonist
RO5263397, or RO-5263397, is a trace amine-associated receptor 1 (TAAR1) partial or full agonist which is used in scientific research. It is the most
RO5263397
Any entity that can be measured
larger system and the state of the original system is given by the partial trace of the state of the larger system. In quantum mechanics, dynamical variables
Observable
Quantum mechanical system that interacts with a quantum-mechanical environment
_{B}} represents the partial trace over system B and similarly t r S {\displaystyle \mathrm {tr} _{S}} represents the partial trace over system S. Recent
Open_quantum_system
Protein found in humans
Trace amine-associated receptor 1 (TAAR1) is a trace amine-associated receptor (TAAR) protein that in humans is encoded by the TAAR1 gene. TAAR1 is a primarily
TAAR1
Foundational object in quantum communication theory
the partial trace of ρ with respect to the B system: ρ A = Tr B ρ . {\displaystyle \rho ^{A}=\operatorname {Tr} _{B}\;\rho .} The partial trace operation
Quantum_channel
Theory of trace monoids
Book of Traces, (1995) World Scientific, Singapore ISBN 981-02-2058-8 Volker Diekert; Yves Metivier (1997). "Partial Commutation and Traces" (PDF). In
Trace_theory
Tensor in differential geometry
converge. Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric
Ricci_curvature
Physics phenomenon
which is the projection operator onto this state. The state of A is the partial trace of ρT over the basis of system B: ρ A = d e f ∑ j N B ( I A ⊗ ⟨
Quantum_entanglement
Theorem in functional analysis
, the upper bound is achieved. Define the partial trace t r V ( A ) {\textstyle tr_{V}(A)} to be the trace of projection of A {\textstyle A} to V {\textstyle
Min-max_theorem
European citizens and residents born in or with ancestors from Sub-Saharan Africa
African ancestry, or Afro-Europeans, refers to people in Europe who trace full or partial ancestry to Sub-Saharan Africa. In the European Union (EU) as of
Black African diaspora in Europe
Black_African_diaspora_in_Europe
Concept in quantum physics
entanglement entropy is the same regardless of whether one computes partial trace over the A {\displaystyle A} or B {\displaystyle B} subsystem. Many
Entropy_of_entanglement
Amino acid metabolites
Tryptamine While not trace amines themselves, the classical monoamines norepinephrine, serotonin, and histamine are all partial agonists at the human
Trace_amine
Pharmaceutical compound
RO5203648 is a trace amine-associated receptor 1 (TAAR1) partial agonist. It is a potent and highly selective partial agonist of both rodent and primate
RO5203648
Property of states in quantum mechanics
_{A}(\rho _{AB}M_{a}^{x}\otimes I_{B})/p(a|x)} , this latter trace denoting a partial trace over Alice's system. An unsteerable assemblage is one that can
Quantum_steering
"Highly entangled" quantum state of 3 or more qubits
locality. An important property of the GHZ state is that taking the partial trace over one of the three qubits yields Tr 3 [ ( | 000 ⟩ + | 111 ⟩ 2 )
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
Axiomatic approach to quantum field theory
state over A ( M ) {\displaystyle {\mathcal {A}}(M)} , we can take the "partial trace" to get states associated with A ( U ) {\displaystyle {\mathcal {A}}(U)}
Algebraic quantum field theory
Algebraic_quantum_field_theory
Chemical compound
agonist for the trace amine associated receptor 1 (TAAR1). It is a full agonist of the rat, cynomolgus monkey, and human TAAR1, but a partial agonist of the
RO5256390
Upper bound on the knowable information of a quantum state
completely positive trace-preserving maps, S ( X : Q ′ Y ) ≤ S ( X : Q ) {\displaystyle S(X:Q'Y)\leq S(X:Q)} . Additionally, as the partial trace over Q ′ {\displaystyle
Holevo's_theorem
Pharmaceutical compound
low-efficacy partial agonist of the trace amine-associated receptor 1 (TAAR1) which has been used in scientific research. TAAR1 partial agonists like
RO5073012
Object which stores memory addresses in a computer program
wild branch before it takes effect, but also provide a complete or partial trace of its history. An autorelative pointer is a pointer whose value is
Pointer (computer programming)
Pointer_(computer_programming)
≥ 0 {\displaystyle I\otimes \rho _{1}-\rho \geq 0} where ρ1 is the partial trace of ρ with respect to the second system. The dual relation ρ 2 ⊗ I −
Reduction_criterion
Specialized notation for multivariable calculus
{\partial y_{1n}}{\partial x}}\\{\frac {\partial y_{21}}{\partial x}}&{\frac {\partial y_{22}}{\partial x}}&\cdots &{\frac {\partial y_{2n}}{\partial x}}\\\vdots
Matrix_calculus
Class of compounds
entactogens acting as releasers of serotonin and/or other monoamines like MDMA. Trace amines like phenethylamine and tryptamine, as well as the monoamine neurotransmitters
Monoamine_releasing_agent
Minnesotan punk rock band, formed 2001
Landlord (both of whom also played in Rivethead), and later formed Partial Traces also with Brad and Nate. Annie also performs with Panel, Bermuda Squares
The_Soviettes
Equation that describes density changes of a material that is diffusing in a medium
The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian
Diffusion_equation
_{A}\langle j|_{A}} , and similarly for ρ B {\displaystyle \rho ^{B}} (see partial trace). If this initial state is separable (i.e. there's only a single λ j
Purity_(quantum_mechanics)
Type of entropy in quantum theory
larger system, ρ A B E {\displaystyle \rho _{ABE}} , such that the partial trace of ρ A B E {\displaystyle \rho _{ABE}} over E yields ρ A B {\displaystyle
Von_Neumann_entropy
American character actor (born 1951)
Good 2009 The Closer Mr Evans Episode: Power of Attorney 2009 Without a Trace Dr Ken Buford Episode: Labyrinths 2010 Rizzoli & Isles Senator Sam Conway
David_Purdham
Measure of information in quantum information theory
subsystem has its own entropy. The state of the subsystems are given by the partial trace operation. The classical joint entropy is always at least equal to the
Joint_quantum_entropy
Differential geometry measure
{\partial S}{\partial x}}\right)^{2}\right){\frac {\partial ^{2}S}{\partial y^{2}}}-2{\frac {\partial S}{\partial x}}{\frac {\partial S}{\partial y}}{\frac
Mean_curvature
Computer programming for quantum computers
as time evolution, measurement simulation, entanglement monotones, partial trace/transpose, discrete Wigner transforms, stabilizer methods, and tensor-network
Quantum_programming
Interaction of a quantum system with a classical observer
initial state is pure, the state at a later time, found by taking the partial trace of the joint system-environment state, will be mixed. This phenomenon
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Data table used to control program flow
depending upon instruction type) at each stage to record a full or partial trace of the actual program flow for debugging purposes, hot spot detection
Control_table
Tensor used in general relativity
geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian
Einstein_tensor
Physical phenomenon
_{12}\circ \Phi )(\rho \otimes \omega )=\rho \,,} where Tr12 is the partial trace operation with respect systems 1 and 2, and ∘ {\displaystyle \circ }
Quantum_teleportation
Study of the relations between thermodynamics and quantum mechanics
system-bath interaction. The state of the system is obtained from a partial trace over the combined system and bath: ρS(t)=TrB(ρSB(t)). Reduced dynamics
Quantum_thermodynamics
Algonquin actor, entertainer and wilderness guide
graduated valedictorian of his class of 1902. Perley's family roots can be traced back to the Maliseet Reservation in Tobique, New Brunswick, Canada. His
Chief_Henry_Red_Eagle
Formula for the derivative of a matrix determinant
{\partial \det(A) \over \partial A_{ij}}=\operatorname {adj} (A)_{ji}=\operatorname {adj} (A)_{ij}^{T}\Longrightarrow {\partial \det(A) \over \partial A}=\operatorname
Jacobi's_formula
French classical harpist
habanera. With Christian Lardé. Arion Paris Maurice Ravel, collection "Sur les traces de…". CD, With Christian Lardé (flute) and Guy Deplus (clarinet). Orchestre
Marie-Claire_Jamet
Algorithm in quantum information theory
tr C ( ρ ) {\displaystyle \operatorname {tr} _{C}(\rho )} is the partial trace operation on the reset qubit C {\displaystyle C} , and ρ ε b {\displaystyle
Algorithmic_cooling
American novelist and abolitionist
of Catholic nuns. Her Gems of the Bog: A Tale of Irish Peasantry (1869) traces the lives of the Sheenan family through various trails until their emigration
Jane_Dunbar_Chaplin
Measure of unpredictability of outcomes
Tr ∗ {\displaystyle \operatorname {Tr} ^{*}} is the adjoint of the partial trace over A {\displaystyle A} . The action of Tr ∗ {\displaystyle \operatorname
Min-entropy
Technique used to optimize the execution of a program at runtime
operations is called a trace. The trace is then optimized and compiled to machine code. When this loop is executed again, the compiled trace is called instead
Tracing just-in-time compilation
Tracing_just-in-time_compilation
American actress and model (1977-2009)
bruises) and with high doses of the drug GHB in her system, together with trace amounts of cocaine. A witness testified that Tang had been a regular user
Felicia_Tang
Genus of extinct avialan
contains a single species, Zhengheornis buyu, known from a partial skeleton with feather traces, preserved on a slab and counterslab. The Zhengheornis fossil
Zhengheornis
Vector operator in vector calculus
=\left({\frac {\partial }{\partial x}},{\frac {\partial }{\partial y}},{\frac {\partial }{\partial z}}\right)\cdot (F_{x},F_{y},F_{z})={\frac {\partial F_{x}}{\partial
Divergence
Application layer protocol
premature close would leave the client with partial content yet the client would not know it is partial. HTTP/1.1 introduced and later versions provide:
HTTP
Italian film actress
Hope (1950) The Forbidden Christ (1951) Rome 11:00 (1952) The Eyes Leave a Trace (1952) Sunday Heroes (1952) Human Torpedoes (1954) Storm (1954) Enrico Lancia
Elena_Varzi
Generalization of strings in computer science
science, a trace is an equivalence class of strings, wherein certain letters in the string are allowed to commute, but others are not. Traces generalize
Trace_monoid
British colonial governor and journalist (1879–1953)
local disputes and to clamp down on banditry and drug trafficking. He also traced the remains of a Roman and Byzantine settlement in northern Sinai, and by
Claude_Scudamore_Jarvis
American actress
Special Victims Unit Carrie Huitt 1 episode: "Futility" 2003 Without a Trace Sarah Sellars 1 episode: "Confidence" 2003 Two and a Half Men Wendy 1 episode:
Myndy_Crist
Class of games in quantum game theory
( Z ) {\displaystyle \operatorname {Tr} _{\mathcal {X}}(Z)} is the partial trace operator. The referee outputs a {\displaystyle a} with probability ⟨
Quantum_refereed_game
Filipino diaspora
(Filipino: Pilipino sa ibayong-dagat) is a person of full or partial Filipino origin who trace their ancestry back to the Philippines but are living and
Overseas_Filipinos
Extinct clade of armored dinosaurs
large herbivore equipped with spikes were uncovered in England; the first partial stegosaurian skeleton known. They were named Omosaurus by Richard Owen
Stegosauria
American radio program
and producer of Shibuya Airwaves. Shibuya Airwaves origins could also be traced back to eigoMANGA's publicized fan petition to bring Japanese rock groups
Shibuya_Airwaves
Invariant in mathematics
={\begin{vmatrix}{\frac {\partial }{\partial x_{11}}}&\cdots &{\frac {\partial }{\partial x_{1n}}}\\\vdots &\ddots &\vdots \\{\frac {\partial }{\partial x_{n1}}}&\cdots
Transvectant
Function in thermodynamics and statistical physics
_{i}\left[{\frac {\partial }{\partial \rho _{i}}}\left(-k_{\text{B}}\rho _{i}\ln \rho _{i}\right)\delta \rho _{i}-{\frac {\partial }{\partial \rho _{i}}}\left(\lambda
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Notion in statistics
{\partial \mu }{\partial \theta _{m}}}&={\begin{bmatrix}{\dfrac {\partial \mu _{1}}{\partial \theta _{m}}}&{\dfrac {\partial \mu _{2}}{\partial \theta
Fisher_information
American actress and singer (born 1957)
guest-starring in shows like JAG (2004), Desperate Housewives (2006), Without a Trace (2008), Major Crimes (2013) and Young Sheldon (2019). Freedman has also
Winifred_Freedman
A , B , Λ ) {\displaystyle (A,B,\Lambda )} . We will represent the partial trace of ϱ A , B , Λ {\displaystyle \varrho _{A,B,\Lambda }} with respect
Squashed_entanglement
Principle in forensics and cyber security
fingerprints – whole or partial. Locard's Principle also holds in computer forensics, where committing cyber crime will result in a digital trace being left behind
Locard's_exchange_principle
Vector space of functions in mathematics
W^{1-{\frac {1}{p}},p}(\partial \Omega ).} Intuitively, taking the trace costs 1/p of a derivative. The functions u in W1,p(Ω) with zero trace, i.e. Tu = 0, can
Sobolev_space
English actor (1912–1982)
(uncredited) Waterfront (1950) – Engineer Blackout (1950) – Mickey Garston No Trace (1950) – Mike Fenton The Clouded Yellow (1950) – Superintendent Ross Circle
Michael_Brennan_(actor)
Rock formation in New York
flow was likely channelized, as evidence from the large variability in trace elements. Fluid flow induced ion mobility and plasticity, as well as enriching
Gore_Mountain_Garnet
Ontological thesis
There are a few philosophers who argue for what could be considered a partial nihilism, or what has been called quasi-nihilism, which is the position
Mereological_nihilism
Square root of the determinant of a skew-symmetric square matrix
{\partial ^{2}\operatorname {pf} (A)}{\partial x_{i}\partial x_{j}}}={\frac {1}{2}}\operatorname {tr} \left(A^{-1}{\frac {\partial ^{2}A}{\partial x_{i}\partial
Pfaffian
Chemical compound
selective agonist for the trace amine-associated receptor 1 (TAAR1), with no significant activity at other targets. It is a partial agonist or near-full agonist
RO5166017
Icelandic film actor (born 1963)
Grjóni Pearls and Swine (1997) – Viktor Count Me Out (1997) – Hilmar No Trace (1998) – Óli Slurpinn & Co. (1998, short) Angels of the Universe (2000)
Ingvar_Eggert_Sigurðsson
British mountaineer (1902–1924)
mountain's Northeast Ridge, and were last seen alive below the summit. Irvine's partial remains were discovered in 2024. Irvine was born in Birkenhead, Cheshire
Andrew_Irvine_(mountaineer)
American actress, model, and dancer
guest appearances on award-winning shows such as CSI: Miami, Without a Trace, NCIS: Los Angeles and Parks and Recreation. Today, she continues to work
Katerina_Mikailenko
Theorem of quantum information processing
a Hilbert space H A ⊗ H B {\displaystyle H_{A}\otimes H_{B}} whose partial traces are Tr A ρ A B = ρ i {\displaystyle \operatorname {Tr} _{A}\rho _{AB}=\rho
No-broadcasting_theorem
TAAR1 agonist
RG-7351 is a trace amine-associated receptor 1 (TAAR1) partial agonist that is or was under development for the treatment of major depressive disorder
RG-7351
Impossible object
triangle (right) is created by overlapping the two parts. The first two partial views of the Penrose triangle are individually perceptible, whereas the
Penrose_triangle
Indian actor based in North America
in many television shows, including The Mentalist, Eli Stone, Without a Trace, The Sopranos, Sex and the City, NCIS, Anger Management, The Middle, Rules
Ajay_Mehta
days, which decays into 218 Po. Six isotopes of radon, 217-222Rn, occur in trace quantities in nature as decay products of, respectively, 217At, 218At, 223Ra
Isotopes_of_radon
Type of evidence of physical contact
Trace evidence occurs when objects make contact, and material is transferred. This type of evidence is usually not visible to the naked eye and requires
Trace_evidence
Mushroom anatomy
mushrooms have partial veils which are evanescent, which are so thin and delicate that they disappear after they rupture, or leave merely a faint trace on the
Partial_veil
American actor
(2002) American Dreams (2003) The Guardian (2003) CSI (2004) Without a Trace (2004) CSI: Miami (2006) CSI: NY (2007) 24 (season 7, 2009) Full Circle
Mark_Kiely
Differential operator in mathematics
{1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}-{\frac {\partial ^{2}}{\partial x^{2}}}-{\frac {\partial ^{2}}{\partial y^{2}}}-{\frac {\partial ^{2}}{\partial z^{2}}}
Laplace_operator
Relative deformation of a physical body
{{\tfrac {\partial u_{y}}{\partial x}}dx}{dx+{\tfrac {\partial u_{x}}{\partial x}}dx}}={\frac {\tfrac {\partial u_{y}}{\partial x}}{1+{\tfrac {\partial u_{x}}{\partial
Strain_(mechanics)
Method of data analysis
and let 𝜮y=𝐁′𝜮𝐁 be the variance-covariance matrix for y. Then the trace of 𝜮y, denoted tr(𝜮y), is maximized by taking 𝐁=𝐀q, where 𝐀q consists
Principal_component_analysis
Jurassic-era geologic formation in Switzerland
to properly confirm the inclusion in the genus Pseudorhina P. sp. One partial tooth Pseudorhina tooth displaying a unique morphology, however too fragmentary
Reuchenette_Formation
American actor (born 1945)
with Money" 2007 Brothers & Sisters Milo Peterman 3 episodes Without a Trace Byron Carlton Episode: "Run" 2007–2011 Damages Phil Grey Recurring cast;
Michael_Nouri
Prime Minister of Israel (1996–1999; 2009–2021; 2022–present)
urging the resumption of peace talks, on 25 November Netanyahu announced a partial 10-month settlement construction freeze. It had no significant effect on
Benjamin_Netanyahu
Italian actor (1946–2019)
IV (1984) The Inquiry (1986) The Professor (1986) The Moro Affair (1987) Traces of an Amorous Life (1990) The Amusements of Private Life (1990) Chimera
Luciano_Bartoli
Mapping theorem in topology
triangulable topological space X {\displaystyle X} to itself by means of traces of the induced mappings on the homology groups of X {\displaystyle X} .
Lefschetz_fixed-point_theorem
travel, tourism, insurance
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