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Metric in quantum mechanics
especially quantum information and the study of open quantum systems, the trace distance is a metric on the space of density matrices and gives a measure of
Trace_distance
Term in quantum mechanics
,\sigma ),} for any trace-preserving completely positive map E {\displaystyle {\mathcal {E}}} . We can define the trace distance between two matrices
Fidelity_of_quantum_states
inheriting this property from the trace distance. This result and its proof can be found in Dupuis et al. Upper bound: Trace distance can be written as ‖ ρ − σ
Generalized_relative_entropy
von Neumann entropies of two density matrices as a function of their trace distance. It was proved by Koenraad M. R. Audenaert in 2007 as an optimal refinement
Fannes–Audenaert_inequality
Distance from center of Earth to center of Moon
Earth–Moon distance, or distance to the Moon, is the distance from the center of Earth to the center of the Moon. In contrast, the Lunar distance (LD or Δ
Lunar_distance
Measure of quantum entanglement in quantum mechanics
\ldots } (typically with increasing n i {\displaystyle n_{i}} ) in the trace distance, but the sequence E N ( ρ 1 ) / n 1 , E N ( ρ 2 ) / n 2 , … {\displaystyle
Negativity (quantum mechanics)
Negativity_(quantum_mechanics)
Interaction of a quantum system with a classical observer
motivation and justification in terms of measurements. For example, the trace distance between quantum states is equal to the largest difference in probability
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Norm on a vector space of matrices
nature of the trace ( trace ( X Y Z ) = trace ( Y Z X ) = trace ( Z X Y ) {\displaystyle \operatorname {trace} (XYZ)=\operatorname {trace} (YZX)=\operatorname
Matrix_norm
1957 radiological contamination disaster in the Soviet Union
of square kilometers of land, now known as the Eastern Ural Radioactive Trace (EURT). The matter was covered up, and few either inside or outside the
Kyshtym_disaster
Seven segments of the historic Natchez Trace are listed on the National Register of Historic Places (NRHP). Also there are additional NRHP-listed structures
Old Natchez Trace segments listed on the National Register of Historic Places
Old_Natchez_Trace_segments_listed_on_the_National_Register_of_Historic_Places
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
Swimming, cycling, and distance running race
conditioning. The evolution of triathlon as a distinct sport is difficult to trace with precision. Many, including triathlon historian and author Scott Tinley
Triathlon
Set of outdoor ethics
Leave No Trace, sometimes written as LNT, is a set of ethics promoting conservation of the outdoors. Originating in the mid-20th century, the concept
Leave_No_Trace
Rail trail in Louisiana, USA
The Tammany Trace is a rail trail in St. Tammany Parish, Louisiana, occupying a former Illinois Central Railroad corridor. It has been developed into
Tammany_Trace
Physical phenomenon
considered distance measure (classical thresholds for Trace distance, quantum Jensen–Shannon divergence, transmission distance, Bures distance, wootters
Quantum_teleportation
Hiking Association
Appalachian Long Distance Hikers Association is a non-profit organization founded in 1983 to support and promote the interests of long-distance hikers in the
Appalachian Long Distance Hikers Association
Appalachian_Long_Distance_Hikers_Association
List of multi-use recreational trails in the United States
This is a list of notable long-distance trails in the United States, with a minimum length of 30 miles (48 km). National Trails System National Millennium
List of long-distance trails in the United States
List_of_long-distance_trails_in_the_United_States
Trackway
The Vincennes Trace was a major trackway running through what are now the American states of Kentucky, Indiana, and Illinois. Originally formed by millions
Vincennes_Trace
Scenic trail in the United States
Trace Trail is a designated National Scenic Trail in the United States, whose route generally follows sections of the 444-mile (715 km) Natchez Trace
Natchez_Trace_Trail
Long-distance running event of 42.195 kilometres
marathon is a long-distance foot race with a distance of 42.195 kilometres (c. 26.22 mi), usually run as a road race, but the distance can be covered on
Marathon
Use of a pronoun tied to an antecedent
distance. Crucial to understanding resumptive pronouns is grasping the concept of their counterpart: the trace. Since resumptive pronouns and traces may
Resumptive_pronoun
British distance runner and philanthropist
charity fundraiser. He is an elite distance runner, with a number of successes at the marathon and ultramarathon distances. In 2016 he began a 422-day, 15
Robert_Pope_(runner)
Shooting discipline
"The Nomad Rifleman Distance Classification". Extreme Long Range Shooting Book. Retrieved 2026-02-14. Vapor trail and Bullet trace | Sniper Country Vapor
Long_range_shooting
Toughness Townsend (unit) Townsend coefficient Toy model Trace-free Ricci tensor Trace distance Track Imaging Cherenkov Experiment Tracking (particle physics)
Index_of_physics_articles_(T)
Term in quantum information theory
the limit of many uses of the channel. A mixed quantum state is a unit trace, positive operator known as a density operator, and is often denoted by
Classical_capacity
American actor (born 1974)
starred as FBI agent Samantha Spade in the CBS mystery drama Without a Trace. From 2007 to 2009, Kaufman had a recurring role in the fifth, sixth and
Adam_Kaufman_(actor)
Rendering method
tracing, each ray is traced in multiple steps to approximate an intersection point between the ray and a surface defined by a signed distance function (SDF)
Ray_tracing_(graphics)
Paved trail between Hattiesburg and Prentiss, Mississippi, USA
The Longleaf Trace is a 44-mile (71 km) paved pedestrian, equestrian, rollerblade, and bicycle trail between Hattiesburg and Prentiss, Mississippi, United
Longleaf_Trace
Wilderness trail in Kentucky, USA
The Logan Trace was a wilderness trail through central Kentucky, a branch of Daniel Boone's Wilderness Road. It was named after its originator, Colonel
Logan_Trace
Distance measured along the surface of the Earth
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arc length. The formulae in this article
Geographical_distance
Lebanese-American former pornographic film actress (born 1993)
Archived from the original on April 8, 2020. Retrieved August 13, 2019. Cowen, Trace William (August 13, 2019). "Mia Khalifa Reveals She Only Made $12,000 as
Mia_Khalifa
Theory for how the brain handles memory recall
In psychology, multiple trace theory is a memory consolidation model advanced as an alternative model to strength theory. It posits that each time some
Multiple_trace_theory
Ways in which length, distance or range can be measured
metrological traceability. The use of metrological traceability to connect different regimes of measurement is similar to the idea behind the cosmic distance ladder
Length_measurement
Pandemic caused by SARS-CoV-2
geographical areas. The strategy aims to increase the capacity to identify and trace chains of transmission and to identify and manage outbreaks, while also
COVID-19_pandemic
Natural satellite orbiting Earth
of Earth. It orbits around Earth at an average distance of 384,399 kilometers (238,854 mi), a distance roughly 30 times the width of Earth. It completes
Moon
Distance function defined between probability distributions
matrix equal to zero, in which case the trace term disappears and only the term involving the Euclidean distance between the means remains. Let μ 1 , μ
Wasserstein_metric
Third planet from the Sun
calcium (1.5%), and aluminum (1.4%), with the remaining 1.2% consisting of trace amounts of other elements. Due to gravitational separation, the core is
Earth
1978 deaths and disappearance in California
easily have been pushed out of the snowpack it was in. At that time, no trace of the men was found. In June 1978, four of the men's bodies were discovered
Yuba_County_Five
Indian political body
unless sooner dissolved. The history of the West Bengal Legislature can be traced back to 18 January 1862 when under the Indian Councils Act 1861, a 12 Member
West Bengal Legislative Assembly
West_Bengal_Legislative_Assembly
Period of major evolutionary diversification of animal life
previously unknown. Trace fossils consist mainly of tracks and burrows, but also include coprolites (fossil feces) and marks left by feeding. Trace fossils are
Cambrian_explosion
Eighth planet from the Sun
solid surface. Neptune orbits the Sun once every 164.8 years at an orbital distance of 30.1 astronomical units (4.5 billion kilometres; 2.8 billion miles)
Neptune
2022 video game
Callisto Protocol is a 2022 survival horror game developed by Striking Distance Studios and published by Krafton. It was released for PlayStation 4, PlayStation
The_Callisto_Protocol
2021 browser game
people to solve than if they start with words such as "slate", "crane", and "trace". Computer algorithms can consistently solve the puzzle within five of the
Wordle
Star at the centre of the Solar System
at a distance of 24,000 to 28,000 light-years. Its mean distance from Earth is about 1.496×108 kilometres or about 8 light-minutes. The distance between
Sun
Point on the Earth's surface that is directly above the hypocenter in an earthquake
From the first seismograms, as seen in the figure, it was noticed that the trace was divided into two major portions. The first seismic wave to arrive was
Epicenter
1993 studio album by Died Pretty
still distancing himself from the record. He said that after signing to Sony Records on the strength of 1991's Doughboy Hollow, the band delivered Trace, which
Trace_(Died_Pretty_album)
Measure of divergence between populations
Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from
Genetic_distance
the DUAL algorithm invokes a diffusing computation to ensure that all traces of the problematic route are eliminated from the network. At which point
Diffusing_update_algorithm
Transient state of euphoria from physical exertion
PMC 1724404. PMID 11579070. Lindemann L, Hoener MC (2005). "A renaissance in trace amines inspired by a novel GPCR family". Trends Pharmacol. Sci. 26 (5):
Runner's_high
Metric for difference between two colors
In color science, color difference or color distance is the separation between two colors. This metric allows quantified examination of a notion that formerly
Color_difference
Group of islands in the South Atlantic
de France (Mauritius). Thouars made botanical collections and reported traces of human habitation, including fireplaces and overgrown gardens, probably
Tristan_da_Cunha
Galaxy containing the Solar System
bars, one nestled within the other. However, RR Lyrae-type stars do not trace a prominent Galactic bar. The bar may be surrounded by a ring called the
Milky_Way
American record producer and musician (1933–2024)
his father was half Welsh around 15 years ago ... "New DNA test results trace Oprah Winfrey's ancestry to Liberia/Zambia". Zambia News. February 6, 2006
Quincy_Jones
Speed of electromagnetic waves in vacuum
299792458 m/s. This fixed value is used to define the metre as exactly the distance that light travels in vacuum in 1⁄299792458 of a second. The second is
Speed_of_light
There are hundreds of long-distance footpaths in the United Kingdom designated in publications from public authorities, guidebooks and OS maps. They are
List of long-distance footpaths in the United Kingdom
List_of_long-distance_footpaths_in_the_United_Kingdom
Contagious disease caused by SARS-CoV-2
PMID 32788101. Wadman M (April 2020). "How does coronavirus kill? Clinicians trace a ferocious rampage through the body, from brain to toes". Science. doi:10
COVID-19
Device that records the speed and distance of a vehicle
centrefield is the distance trace. The stylus moves up and down with distance travelled, producing a zig-zag pattern, often referred to as a 'V' trace. A complete
Tachograph
Auxiliary scale of a measurement device, used to increase precision
single measured-value pointer, and has for instance ten divisions equal in distance to nine divisions on the main scale. The interpolated reading is obtained
Vernier_scale
Electronic instrument
equipment TDR trace of a transmission line with an open termination TDR trace of a transmission line with a short circuit termination TDR trace of a transmission
Time-domain_reflectometer
Canadian actor (born 1969)
show What I Like About You and a February 2006 appearance on Without a Trace. Priestley has also made several films, his most notable role perhaps[citation
Jason_Priestley
Mars orbiter, part of ExoMars programme
The ExoMars Trace Gas Orbiter (TGO or ExoMars Orbiter) is a collaborative project between the European Space Agency (ESA) and the Russian Roscosmos agency
Trace_Gas_Orbiter
Principle in quantum information theory
mathematically by comparing the trace of σ and the trace of P(σ), with the trace being taken over the subspace HA. Since the trace is only over a subspace, it
No-communication_theorem
Census-Designated Place in Virginia, United States
Air Force/U.S. Army officer and last Tuskegee Airmen cadet pilot graduate Trace McSorley, Washington Commanders quarterback Wilson Pickett, singer David
Ashburn,_Virginia
American alpine skier
her diary. According to prosecutors, the sample showed the presence of a trace amount of cocaine in her blood, and her diary reportedly contradicted her
Spider_Sabich
Large self-illuminated object in space
Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of light. The most prominent
Star
American actor and filmmaker (born 1979)
of television series including Law & Order: Criminal Intent, Without a Trace, Ed, American Dad! and CSI: Crime Scene Investigation. He also co-starred
John_Krasinski
Method of terrestrial locomotion allowing rapid movement on foot
that the ancestors of humankind developed the ability to run for long distances about 2.6 million years ago, probably to hunt animals. Competitive running
Running
American singer and actress (born 1992)
a previous relationship, her mother has two other children, Brandi and Trace. Her father's first child, Christopher Cody, was born in April 1992 and
Miley_Cyrus
2013 disappearance in California
law‑enforcement officer in the hours before the vehicle was discovered, no trace of him was found at the scene, and extensive searches of the surrounding
Disappearance of Bryce Laspisa
Disappearance_of_Bryce_Laspisa
Criminal gang in Birmingham, England (1880s – 1920s)
battery, stabbing, and strangling. The origins of this subculture can be traced back to the 1850s, a time when Birmingham's streets were filled with gambling
Peaky_Blinders
Annual experimental event in Nevada, US
radical self-expression, communal effort, civic responsibility, leaving no trace, participation, and immediacy. Burning Man features no headliners or scheduled
Burning_Man
Sixth planet from the Sun
Jupiter, having a small rocky core surrounded by hydrogen and helium, with trace amounts of various volatiles. While standard planetary models assume Saturn's
Saturn
Extinct burrowing sea creature
it. The hypothesis supported by Seilacher, that the burrows we find are trace fossils of a worm-like animal, is supported by several features of the burrows
Paleodictyon_nodosum
Gigabit passive optical network system
signal levels. In contrast to ADSL technology, which deteriorates as the distance between the central office and the household rises, with severe signal
GPON
Perceived separation between objects or contexts
estimate it (psychic distance stimuli: Dow & Karunaratna, 2006). The business origins of the "psychic distance" idiom can be traced back to research conducted
Psychic_distance
3D computer graphics rendering method
the use of cubes and taxicab distance can be used to render voxel volumes. In volumetric ray marching, each ray is traced so that color and/or density
Ray_marching
Mass transferring brown dwarf binary
component is estimated to have a radius of 0.9–1.4 Jupiter radii. Hydrogen and trace amounts of sodium and potassium in the brown dwarfs' atmospheres have been
ZTF_J1239+8347
NASA space probe launched in 1977
and to transmit data to Earth. Real-time distance and velocity data are provided by NASA and JPL. At a distance of 172.59 AU (25.8 billion km; 16.0 billion mi)
Voyager_1
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
Four-dimensional analogue of the cube
tesseract in Wiktionary, the free dictionary. The Oxford English Dictionary traces the word tesseract to Charles Howard Hinton's 1888 book A New Era of Thought
Tesseract
48 states of the US apart from Alaska and Hawaii
and all the insular areas in the Caribbean and the Pacific. The greatest distance on a great-circle route entirely within the contiguous U.S. is 2,802 miles
Contiguous_United_States
American actor and model (born 1985)
Shapiro in Saving Grace, Ryan Stephenson in Bones, Jeff Ellis in Without a Trace, Seiji Amasawa in the English dub of Whisper of the Heart, and Kevin Mather
David_Gallagher
Seventh planet from the Sun
a rocky core, and a thick hydrogen and helium atmosphere surrounds it. Trace amounts of hydrocarbons (thought to be produced via hydrolysis) and carbon
Uranus
Term in quantum information theory
\|_{1}} denotes the trace norm. The diamond norm induces the diamond distance, which in the particular case of completely positive, trace non-increasing maps
Diamond_norm
Educational learning method using computer algorithms and AI
start of the work on adaptive and intelligent learning systems is usually traced back to the SCHOLAR system that offered adaptive learning for the topic
Adaptive_learning
Chemical element with atomic number 94 (Pu)
is the element with the highest atomic number known to occur in nature. Trace quantities arise in natural uranium deposits when uranium-238 captures neutrons
Plutonium
at a mean point and the plane is normal to the tooth trace. Offset is the perpendicular distance between the axes of hypoid gears or offset face gears
List_of_gear_nomenclature
Compact astronomical body
term was used by others around that time. Science writer Marcia Bartusiak traces the term black hole to physicist Robert H. Dicke, who in the early 1960s
Black_hole
American actor
received a Drama Desk Award for his performance in Neil LaBute's play The Distance from Here in 2004. In 2005, he performed in three separate productions:
Logan_Marshall-Green
micrometers to meters in size, and are made almost entirely of water ice, with a trace component of rocky material. Though light reflected from the rings increases
Rings_of_Saturn
Instrument for displaying time-varying signals
deflects the trace downward. The vertical position control moves the whole displayed trace up and down. It is used to set the no-input trace exactly on
Oscilloscope
Film by Benoît Delhomme
for her heart, but an autopsy carried out at Alice's request reveals no trace of that medication in her bloodstream. Alice suspects that Céline has been
Mothers'_Instinct_(2024_film)
Radar sweep display
display, with the distance from it and height above ground drawn as concentric circles. As the radar antenna rotates, a radial trace on the PPI sweeps
Plan_position_indicator
Geographic coordinate specifying north-south position
the modern literature).) Legendre, A. M. (1806). "Analyse des triangles tracés sur la surface d'un sphéroïde". Mém. Inst. Nat. Fr. 1st semester: 130–161
Latitude
Speakers of Austronesian languages
the Philippines and proposed that they arrived to the islands via long-distance voyaging. The Spanish philologist Lorenzo Hervás later devoted a large
Austronesian_peoples
Welsh Government COVID-19 service
Test, Trace, Protect is a government-funded service in Wales, first published on 13 May 2020 by the Welsh Government to track and help prevent the spread
Test,_Trace,_Protect
Greek mythological hero
Pyrrha, the Aethiopis and Iliupersis by Arctinus of Miletus), there is no trace of any reference to his general invulnerability or his famous weakness at
Achilles
1912 maritime disaster
engines to be put "full astern". The two ships avoided a collision by a distance of about 4 feet (1.2 m). The incident, as well as a subsequent stop to
Sinking_of_the_Titanic
Medical diagnostic method
"trace alternant" activity. "Discontinuous" electrical activity describes sharp bursts of electrical activity followed by low frequency waves; "trace alternant"
Fetal_EEG
Traditional Chinese unit of distance
or ri (Chinese: 里, lǐ, or 市里, shìlǐ) is a traditional Chinese unit of distance. The li has varied considerably over time but was usually about one third
Li_(unit)
TRACE DISTANCE
TRACE DISTANCE
Girl/Female
English American
from Thracia.
Female
English
Feminine variant spelling of English unisex Tracy, TRACI means "place of Thracius."
Girl/Female
Greek American French
Reaper; from Therasia.
Surname or Lastname
English
English : probably from Middle English, Old French brace ‘arm’, also denoting a piece of armor covering the arm. In most cases it is probably a metonymic occupational name for a maker or seller of armor, specifically armor designed to protect the upper arms, but it could also have been a nickname for someone with strong arms (compare Armstrong) or a deformed or otherwise noticeable arm.
Female
English
Feminine variant spelling of English unisex Tracy, TRACIE means "place of Thracius."
Male
English
English surname transferred to unisex forename use, from a Norman baronial name TRACY means "place of Thracius."
Girl/Female
Latin American English Irish
Grace.
Girl/Female
English
from Thracia.
Boy/Male
Anglo Saxon American Latin Greek English French
Brave.
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Surname or Lastname
English
English : nickname from Middle English, Old French grace ‘charm’, ‘pleasantness’ (Latin gratia).English : from the female personal name Grace, which was popular in the Middle Ages. This seems in the first instance to have been from a Germanic element grīs ‘gray’ (see Grice 1), but was soon associated by folk etymology with the Latin word meaning ‘charm’.
Male
English
Short form of English unisex Tracy, TRACE means "place of Thracius."
Girl/Female
Greek American
Reap; from Therasia.
Female
English
Feminine variant spelling of English unisex Tracy, TRACEE means "place of Thracius."
Surname or Lastname
English
English : perhaps a variant of Treece.
Girl/Female
American, Arabic, Australian, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Irish, Jamaican, Latin, Muslim, Portuguese, Swedish
Mercy; God's Favor; Grace; Grace of God; Kindness; Thanks; Love; Favour; Blessing; Charm; Good will
Male
English
Variant spelling of English unisex Tracy, TRACEY means "place of Thracius."
Surname or Lastname
English (Kent)
English (Kent) : perhaps a variant of Treece.Altered spelling of German Treis, a topographic name for someone who lived by or owned an uncultivated piece of land used as pasture, from Middle Low German drīsch ‘fallow land’, or a habitational name from a place named with this word (in Hessian dialect treis), in Hesse or on the Mosel river. Alternatively, in some instances it may be from a short form of the personal name Andreas (see Andrew).
Boy/Male
Anglo Saxon American Greek
Brave.
Boy/Male
Anglo Saxon American English French
Brave.
TRACE DISTANCE
TRACE DISTANCE
Girl/Female
Irish
Female
English
 Variant spelling of English Lorri, LORI means "land of the people of Lothar." Compare with another form of Lori.
Surname or Lastname
English
English : variant of Atwell.
Boy/Male
Celtic
Mythical hunter god.
Girl/Female
Norse German Teutonic
Rules.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lotus
Boy/Male
Sikh
Fighter of Love and truth
Girl/Female
Tamil
Boy/Male
Indian, Punjabi, Sikh
Love for Charm
Boy/Male
Polish
Good.
TRACE DISTANCE
TRACE DISTANCE
TRACE DISTANCE
TRACE DISTANCE
TRACE DISTANCE
n.
A mark or impression left by the foot, either of man or beast; trace; vestige; footprint.
v.
A company of men engaged in the same occupation; thus, booksellers and publishers speak of the customs of the trade, and are collectively designated as the trade.
n.
One who, or that which, traces.
v. t.
To cause to contend in a race; to drive at high speed; as, to race horses.
v. t.
Hence, to follow the trace or track of.
v.
Track; trace.
v. t.
To trace by scent; to track; -- a hunting term.
n.
A tract or area, as of land.
v. t.
A mark left by anything passing; a track; a path; a course; a footprint; a vestige; as, the trace of a carriage or sled; the trace of a deer; a sinuous trace.
v. t.
To add grace notes, cadenzas, etc., to.
n.
A mark left by something that has passed along; as, the track, or wake, of a ship; the track of a meteor; the track of a sled or a wheel.
v. t.
To follow the tracks or traces of; to pursue by following the marks of the feet; to trace; to trail; as, to track a deer in the snow.
v. t.
To mark out; to draw or delineate with marks; especially, to copy, as a drawing or engraving, by following the lines and marking them on a sheet superimposed, through which they appear; as, to trace a figure or an outline; a traced drawing.
v. t.
To trace out; to track; also, to draw out; to protact.
imp. & p. p.
of Trace
n.
Course; way; as, the track of a comet.
v.
Continuity or extension of anything; as, the tract of speech.
v. t.
To supply with heavenly grace.
v. t.
To run a race with.
v.
The trade winds.