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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
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)
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
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
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
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
similar: the density matrix of the message systems should be close in trace distance to a simulator distribution. Allowing quantum resources can never increase
Private simultaneous message passing
Private_simultaneous_message_passing
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
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
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
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
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
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
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
Physical phenomenon
considered distance measure (classical thresholds for Trace distance, quantum Jensen–Shannon divergence, transmission distance, Bures distance, wootters
Quantum_teleportation
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
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
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
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
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)
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
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
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
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)
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)
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
Void between celestial bodies
atoms; most of the remainder consists of helium atoms. This is enriched with trace amounts of heavier atoms formed through stellar nucleosynthesis. These atoms
Outer_space
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
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
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
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
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
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
Method of terrestrial locomotion allowing rapid movement on foot
recorded games took place in 776 BCE. Running in Ancient Greece can be traced back to these games of 776 BCE. ...I suspect that the sun, moon, earth,
Running
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
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
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
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
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
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
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
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)
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
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)
Observed discrepancy in galactic angular momenta
orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically as a plot
Galaxy_rotation_curve
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
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
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
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
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
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
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
1996 British film by John Henderson
state-of-the-art technology, Dempsey scans the whole loch, and is unable to find any trace of the monster. When he declares the end of the myth, Adrian angrily berates
Loch_Ness_(film)
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
American actor (born 1976)
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
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
Speed of electromagnetic waves
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
American actress (born 1979)
throughout the 2000s, on series such as Law & Order: Criminal Intent, Without a Trace, and CSI. For her portrayal of Bonnie Crasnoff—a patient who is severely
Monica_Keena
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
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
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
Type of trace fossil
significant as a very old megascopic fossil, and thus eukaryote. It is a trace fossil and thus evidence of activity, rather than a body fossil. Myxomitodes
Myxomitodes
American drummer (1954–1992)
atherosclerosis resulting from cocaine use, and stated that tests found no trace of pesticides in Porcaro's system. Friends and relatives have rejected this
Jeff_Porcaro
Galaxy containing the Solar System
two colure circles passing through both poles. The English term can be traced back to a story by Geoffrey Chaucer c. 1380: See yonder, lo, the Galaxyë
Milky_Way
Geographic coordinate specifying north-south position
distance from the equator to the pole is m p = m ( π 2 ) {\displaystyle m_{\mathrm {p} }=m\left({\frac {\pi }{2}}\right)\,} For WGS84 this distance is
Latitude
Yemeni Hashemite Arab clan
Al-Houthi is an aristocratic Yemeni tribe who trace their origins to the Banu Hashim, descending directly from Hasan ibn Ali. The al-Houthi family being
Al-Houthi_family
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
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
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
2002 British TV series or programme
Chris Terrill – came from several countries and nationalities. The crew traced Cook's footsteps from one historical landmark to another. All of the volunteers
The_Ship_(TV_series)
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
Warm-blooded animals with wings and feathers
York: Pi Press. ISBN 0-13-186266-9. Borenstein, Seth (31 July 2014). "Study traces dinosaur evolution into early birds". Associated Press. Archived from the
Bird
Conjecture on zeros of the zeta function
a rank-trace inequality derived from von Neumann's trace inequality. The logical core of the proof, including the matrix inequalities and trace asymptotics
Riemann_hypothesis
American swimmer (1905–2003)
than two hours." Ferguson, Lee. "Developments of Screen and Stage Shows Traced in Career of E. L. Hyman", Motion Picture News, New York, January 7, 1928
Gertrude_Ederle
British mountaineer (1902–1924)
that his ice axe bounced off a rock and killed him. The search revealed no trace of the two Vest Pocket Kodak cameras that Irvine's diaries said he and Mallory
Andrew_Irvine_(mountaineer)
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
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
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
American actor (born 1959)
Northern Exposure, Law & Order, Law & Order: Criminal Intent, Without a Trace, CSI: Crime Scene Investigation, The West Wing, and the short-lived sitcom
Dylan_Baker
Australian actress (born 1988)
life". Browining appeared in Andrea Pallaoro's 2022 drama Monica, alongside Trace Lysette, Patricia Clarkson and Adriana Barraza, replacing Anna Paquin who
Emily_Browning
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
Way of visually representing the orientation of objects in 3D space
net so the trace corresponds to an arc of the net; the pole is situated on an arc, and the angular distance between this arc and the trace is 90°. Consider
Pole_figure
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
1988 aircraft bombing over Scotland
had apparently intended the plane to crash into the sea, destroying any traceable evidence, but its explosion over land left a trail of evidence. The fuselage
Pan_Am_Flight_103
American actor and musician
CMT August 8, 2011 and reached no. 1 on their Today's Top Videos chart . Trace Adkins released a song written by Kane called "Happy Man" on his 2010 album
Christian_Kane
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
Hypothetical invisible cosmic material
not trace the decline expected from Keplerian orbits. As more sensitive receivers became available, Roberts & Whitehurst (1975) were able to trace the
Dark_matter
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
Brackish lake in Vouliagmeni, Greece
an underwater cave never fully explored, as its end seems impossible to trace even by employing sonar detection. Many underwater expeditions have been
Lake_Vouliagmeni
American minister, father of Marvin Gaye (1914–1998)
what he had done. After results of Marvin's autopsy showed that he had traces of cocaine and PCP in his system, and pictures were shown of Gay after he
Marvin_Gay_Sr.
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
Country in northern Europe
and austrvegr "eastern way" (from austr) for the Baltic. The earliest traces of human occupation in Norway are found along the coast, where the huge
Norway
First planet from the Sun
the Sun and the smallest in the Solar System. It is a rocky planet with a trace atmosphere and a surface gravity slightly higher than that of Mars. The
Mercury_(planet)
American murder case
(48 km) away from the Wetterling home and the abduction site and a short distance from where Heinrich was living in 1989. On September 3, the remains were
Murder_of_Jacob_Wetterling
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
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