The Turing machine, developed by Alan Turing in the 1930s, is a theoretical device that consists of tape of unlimited length that is divided into little squares. Each square can either hold a symbol (1 or 0) or be left blank. A read-write device reads these symbols and blanks, which gives the machine its instructions to perform a certain program. Does this sound familiar? Well, in a quantum Turing machine, the difference is that the tape exists in a quantum state, as does the read-write head. This means that the symbols on the tape can be either 0 or 1 or a superposition of 0 and 1; in other words the symbols are both 0 and 1 (and all points in between) at the same time. While a normal Turing machine can only perform one calculation at a time, a quantum Turing machine can perform many calculations at once.
Today's computers, like a Turing machine, work by manipulating bits that exist in one of two states: a 0 or a 1. Quantum computers aren't limited to two states; they encode information as quantum bits, orqubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers.
This superposition of qubits is what gives quantum computers their inherent parallelism. According to physicist David Deutsch, this parallelism allows a quantum computer to work on a million computations at once, while your desktop PC works on one. A 30-qubit quantum computer would equal the processing power of a conventional computer that could run at 10 teraflops (trillions of floating-point operations per second). Today's typical desktop computers run at speeds measured in gigaflops (billions of floating-point operations per second).
Quantum computers also utilize another aspect of quantum mechanics known as entanglement. One problem with the idea of quantum computers is that if you try to look at the subatomic particles, you could bump them, and thereby change their value. If you look at a qubit in superposition to determine its value, the qubit will assume the value of either 0 or 1, but not both (effectively turning your spiffy quantum computer into a mundane digital computer). To make a practical quantum computer, scientists have to devise ways of making measurements indirectly to preserve the system's integrity. Entanglement provides a potential answer. In quantum physics, if you apply an outside force to two atoms, it can cause them to become entangled, and the second atom can take on the properties of the first atom. So if left alone, an atom will spin in all directions. The instant it is disturbed it chooses one spin, or one value; and at the same time, the second entangled atom will choose an opposite spin, or value. This allows scientists to know the value of the qubits without actually looking at them.......
May 4, 1935 New York Timesarticle headline regarding the imminent EPR paper.
The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen.[1] In this study, they formulated the EPR paradox(Einstein, Podolsky, Rosen paradox), a thought experiment that attempted to show that quantum mechanical theory wasincomplete. They wrote: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete."[1]
However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Following the EPR paper, Erwin Schrödinger wrote a letter (in German) to Einstein in which he used the wordVerschränkung (translated by himself as entanglement) "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."[15] He shortly thereafter published a seminal paper defining and discussing the notion, and terming it "entanglement." In the paper he recognized the importance of the concept, and stated:[2] "I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."
Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity.[16] Einstein later famously derided entanglement as "spukhafte Fernwirkung"[17] or "spooky action at a distance."
The EPR paper generated significant interest among physicists and inspired much discussion about the foundations of quantum mechanics (perhaps most famously Bohm's interpretation of quantum mechanics), but produced relatively little other published work. So, despite the interest, the flaw in EPR's argument was not discovered until 1964, when John Stewart Bell proved that one of their key assumptions, the principle of locality, was not consistent with the hidden variables interpretation of quantum theory that EPR purported to establish. Specifically, he demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.[18] His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Freedman and Clauser in 1972[19] and Aspect's experiments in 1982.[20] They have all shown agreement with quantum mechanics rather than the principle of local realism. However, the issue is not finally settled, as each of these experimental tests has left open at least one loophole by which it is possible to question the validity of the results.
The work of Bell raised the possibility of using these super strong correlations as a resource for communication. It led to the discovery of quantum key distribution protocols, most famously BB84 by Bennet and Brassard and E91 by Artur Ekert. Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security.
David Kaiser of MIT mentioned in his book, How the Hippies Saved Physics, that the possibilities of instantaneous long-range communication derived fromBell's theorem stirred interest among hippies, psychics, and even the CIA, with the counter-culture playing a critical role in its development toward practical use.[21]
Aug 28, 2008 - “Can you give me a simple, concrete explanation of how quantum computers work?” I've been asked this question a lot. I worked on quantum ...
India's most wanted man, Dawood Ibrahim, poses for photos in this undated photo at an unknown location. Source: AP
(Bloomberg) -- When last seen in public some 25 years ago, Dawood Ibrahim was a chubby man with oversized sunglasses and a droopy mustache. His fondness for betting on cricket matches and keeping company with Indian movie stars has attracted police investigations and tabloid headlines.
Ibrahim is also one of India’s most-wanted terrorists. He’s linked to bombings that killed hundreds of innocent men and women in his native country. India and the U.S. accuse him of financing Pakistani militants who killed hundreds more, as well as brokering a deal with al-Qaeda to allow the group access to his smuggling routes.
And all available evidence culled from accounts on the ground in India and Pakistan, buttressed by reports from the U.S. and United Nations, point to one conclusion: Ibrahim is living in Pakistan.
Just as Osama bin Laden’s death at a house down the road from the Pakistan Military Academy set off fierce debate about the nation’s commitment to fighting terrorism, Ibrahim has become a symbol of why Pakistan’s neighbors often don’t take its public statements about uprooting militants seriously.
The cost of that reluctance was underlined in blood last week when Pakistani Taliban militants murdered 152 people, including 134 children, in the nation’s northwest city of Peshawar. In the aftermath of that slaughter, Prime Minister Nawaz Sharif vowed to wipe out every last terrorist from Pakistani soil.
There are no indications that Ibrahim, thought by police to be 58 years old, had anything to do with the carnage in Peshawar. In fact, officials in Islamabad insist, as they did with bin Laden, that he isn’t in their country at all.
‘No Information’
“Pakistan has no information about his whereabouts,” Tasnim Aslam Khan, a foreign ministry spokeswoman in the capital, said by phone on Dec. 20. Switching between Urdu and the lightly-accented, crisp English of her country’s elite, she continued: “He’s an Indian national. Sometimes we hear he’s in Bangkok, and sometimes elsewhere.” Maj. General Asim Bajwa, chief spokesman for Pakistan’s military, didn’t respond to text messages or an e-mail seeking comment.
Ibrahim’s story personifies the violent and, often, shadowy nature of relations between India and Pakistan, which together hold about a fifth of the world’s people. The two nations were cleaved from one another by physical partition when British colonial rule ended in 1947, leaving hundreds of thousands dead just eight years before Ibrahim’s birth. The region now contains a tempest of corrupt officials, religious zealots and competing business interests that can be unpredictable -- men who pull triggers for you today can turn their guns back on you tomorrow.
Simply ‘Dawood’
The son of a Mumbai police constable, Ibrahim worked his way up from smalltime street thug to the city’s most powerful gang leader. Police in Mumbai say that he ran a protection and smuggling racket before moving to Dubai in the 1980s. He is known to readers of Indian newspapers simply as “Dawood,” a main inspiration for the Mafioso archetype in Bollywood films.
A former aide of Ibrahim, wearing a fat diamond and ruby ring on his finger, said his old boss had a taste for expensive cigarettes, nice cars and Italian suits. These days, he said, Ibrahim can’t travel as far as he used to.
Photographs of Ibrahim, whose full name is Dawood Ibrahim Kaskar, are easily accessible on the Internet. Despite facing criminal charges from India, standing accused by the U.S. and the UN of terrorist activities, and being listed by Interpol, Ibrahim remains free -- and thought to be not far from his hometown.
Karachi Homes
The alleged mass murderer has long done business in Karachi, a Pakistani megacity that like Mumbai sits on the Arabian Sea. The twin metropolises are some 540 miles from one another on the same coastline, roughly the distance of a quick flight from New York to Charlotte, North Carolina. Ibrahim’s presence there, complete with stories of large homes and lavish parties, was confirmed by Bloomberg News in conversations this year with a half dozen past associates and witnesses in Karachi and Mumbai, as well as Indian officials. Many asked not to be identified due to fears about their personal safety.
For Indians, the suggestion that they’re still in touch with a man seen by law enforcement as something of a Judas figure -- the son of a cop who betrayed his own country -- could bring trouble. The same is true in Pakistan, where confirming his presence contradicts the official line and might cause an unwelcome visit from intelligence agencies. And then there’s always the risk of offending the man himself.
U.S. Sanctions
As India and the U.S. made political overtures this past year to mend a relationship that had drifted, part of the rapprochement included renewed efforts to squeeze Ibrahim.
Indian Prime Minister Narendra Modi and U.S. President Barack Obama, the leaders of the world’s two largest democracies, issued a statement after a September summit in Washington, D.C. that listed Ibrahim’s organization, known as D Company, among those for which they would seek to jointly “disrupt all financial and tactical support.”
D Company was named a “significant foreign narcotics trafficker” in 2006 under a U.S. anti-narcotics kingpin law. A 2010 Congressional Research Service report said that D Company’s business model includes smuggling humans and money, and selling drugs -- pointing to it as “an example of the criminal-terrorism ‘fusion’ model.”
Indian officials accuse Ibrahim of helping mastermind a dozen bombings and grenade attacks that ripped through Mumbai in March 1993, killing 257 people and wounding 713 in one of the deadliest terrorist attacks in the nation’s history.
Pakistani Passports
After that onslaught, according to U.S. Treasury and UN reports, Ibrahim doled out cash to Lashkar-e-Taiba. The outlawed militant organization is based in Pakistan and opposes India’s presence in Kashmir, a region divided between India and Pakistan and claimed by both. A senior Lashkar-e-Taiba member used money from Ibrahim to “facilitate the July 2006 train bombing in Mumbai,” the UN said in a 2009 report. Those seven blasts left 187 dead and 829 injured. The group also stands accused of carrying out a 2008 commando-style assault on Mumbai that killed 174 people.
The U.S. Treasury has published passport numbers for Ibrahim, including two issued by Pakistan’s government. The U.S. and UN listed addresses in Pakistan that correspond to a series of villas in Karachi and Islamabad obscured by high walls. A street near one was blocked by guards earlier this year. Two trucks of gunmen sat close to another. Business cards left on outer gates didn’t result in calls back.
Policeman’s Son
Retired Lt. General Hamid Gul, who headed Pakistan’s Inter-Services Intelligence agency for a period in the 1980s and said that he became “very popular with the jihadis,” claimed Ibrahim was “probably not involved” in the 1993 Mumbai bombings. He said there was no connection between the agency, known as ISI, and Ibrahim.
As for Ibrahim’s whereabouts, Gul, dressed in a blue cardigan sweater and gray blazer, shrugged. “I don’t know about him,” he said in a February meeting in Islamabad. “They say that he’s in Karachi.”
At Ibrahim’s old south Mumbai neighborhood of Dongri, cramped restaurants sell bone marrow soup and mosques sit among shops selling Korans and bedazzled iPhone covers. One of his brothers, Iqbal Kaskar, still lives up a dim flight of stairs nearby, a location confirmed by a family lawyer. He didn’t respond to requests for comment.
As Ibrahim’s gang rose first in Muslim quarters and then across the city, it maintained cordial ties with the police, said Shamim Hava, a mining businessman involved in regional politics who grew up in the area. “Because his father was a policeman,” he said, “they always had a soft spot for him.”
Spy Agency
Shamsher Khan Pathan, a cop who worked Ibrahim’s neighborhood in the 1980s and retired as assistant commissioner of police for Mumbai in 2012, gave a different reason for why men in uniform left Ibrahim and his men alone: “Money.”
Ibrahim first established a relationship with Pakistan’s ISI spy agency while building his smuggling operations for consumer goods, then gold and finally drugs, according to Indian security officials.
ISI operates as an empire unto itself in Pakistan, beyond the control of any civilian authority. It smoothed the way for Ibrahim to make illegal shipments in the region, said Gopal K. Pillai, who helped oversee security and intelligence agencies as India’s home secretary from 2009 to 2011.
That bond grew tighter as Ibrahim spent time in Dubai, where criminals, businessmen and spies from across the region had space to mix in a murky underworld, Pillai said in a meeting in Delhi late last year.
“Everybody plays one way, two ways, three ways -- and at the end you don’t know what really is the truth,” Pillai said. “But it’s a game which everybody plays. So, he got into that.”
Mumbai Bombings
In December of 1992, a crowd of Hindu nationalists tore down a mosque in northern India. Riots followed between rampaging mobs of Hindus and Muslims that month and the next. Hundreds of people were killed in Mumbai, the majority of them Muslim. Ibrahim was watching.
“He was angry and he was frustrated and he wanted to do something,” said Rakesh Maria, Mumbai’s police commissioner, who has worked in counter-terrorism and made taking down Ibrahim a life’s ambition. “This is where these people, ISI, came into the picture.”
No one interviewed about Ibrahim described him as being a religious ideologue. They attributed his role in the 1993 bombings in varying degrees to a desire for revenge after the bloodshed in Mumbai and the ISI sensing an opportunity to exploit him to strike an old foe. Current and former Indian officials presented Ibrahim’s relationship with the ISI as one of mutual convenience: The spy agency gave safe haven for him personally as well as his broader criminal network, with Ibrahim in return offering financial backing and logistical support to ISI-backed militant groups.
Guns, Grenades
Confessions showed that those picked up after the attacks were tutored in bomb-making and “handling of sophisticated automatic weapons like AK-56 Rifles and handling of hand grenades in Pakistan,” the Supreme Court of India wrote in a 2013 judgment reviewing death sentences for men involved in the bombings. The training circuit, the court said, was “organized and methodically carried out by Dawood Ibrahim” and others.
U.S. officials have kept tabs on Ibrahim over the years, according to diplomatic cables published by WikiLeaks in 2010. One document details a 2004 meeting with an anti-money laundering official in the United Arab Emirates to discuss Ibrahim; another notes allegations that same year of his links with an Islamist group in Indonesia; and a 2009 cable mentions his alleged links to drug trafficking in Mozambique.
‘Global Terrorist’
When answering questions about Ibrahim, U.S. officials are cautious. The U.S. gave Pakistan about $26 billion in overt aid and military reimbursements between 2001 and 2013 even as American drones killed suspected terrorists in the country.
Although the U.S. Treasury named Ibrahim a “Specially Designated Global Terrorist” in 2003 and listed known addresses for him in Karachi, American officials never publicly demanded that Pakistan hand him over.
Asked about Ibrahim earlier this year, the U.S. embassy in Islamabad sent a statement grouping him with Hafiz Saeed, a Pakistan resident who helped create Lashkar-e-Taiba, the militant outfit that Ibrahim allegedly funded. “We encourage the Government of Pakistan to enforce the sanctions against these individuals,” said the statement. The embassy said in October it had nothing to add.
Legitimate Businessman
Last month, Indian Home Minister Rajnath Singh told a conference in New Delhi that Ibrahim had been moved to Pakistan’s border region with Afghanistan after increased diplomatic pressure to have him extradited.
While Ibrahim’s exact address in Pakistan isn’t known, his past wheeling-and-dealing in Karachi left a trail.
Some around the world consider Ibrahim a terrorist, but in Pakistan he’s a legitimate businessman, said a top real estate broker in Karachi, between sips of tea in the lobby of the city’s Marriott.
Ibrahim invests in residential projects and undeveloped plots of land, said the broker, who wore sunglasses indoors and added that he’s advised Ibrahim on past ventures. The money is routed through proxies and the transactions are perfectly legal, he said, adding that Ibrahim hasn’t done anything wrong in Pakistan.
In 2005, Ibrahim’s daughter married the son of famous retired Pakistani cricket player Javed Miandad. News of a ceremony held by Ibrahim’s family in Dubai was splashed across headlines in India. The patriarch apparently didn’t show up.
Seaside Wedding
Miandad’s family later held a quieter function at a hotel in Karachi with a guest list that included Imran Khan, a former captain of Pakistan’s national cricket team and now a top opposition politician.
“Believe me, I never saw Dawood Ibrahim there,” Khan said in an interview. Miandad declined to discuss Ibrahim.
As recently as 2011, Ibrahim hosted a wedding event in Karachi for his son, according to one of the city’s wealthiest businessmen, who attended. The proud father and accused terrorist greeted guests at the wedding hall, decorated by billowing white tent roofs near the Arabian Sea. The site the businessmen named isn’t far from a McDonald’s and a beach-side shopping mall in Pakistan’s financial capital.
Although Ibrahim couldn’t arrange the family event in his hometown of Mumbai, there, under the skies of Karachi, he was safe. For Pakistan’s neighbors, that’s the problem.
17 hours ago - President Ashraf Ghani of Afghanistan in Islamabad, Pakistan, last ... Credit Tyler Hicks/The New York Times ... 15, Abdul Rab Rassoul Sayyaf, a prominent mujahedeen commander, also warned of the perils of getting closer to Pakistan. ... A version of this article appears in print on March 9, 2015, on page ...
Mar 19, 2014 - By CARLOTTA GALL MARCH 19, 2014 ... has evolved in Pakistan has been to make a show of cooperation .... President Karzai of Afghanistan warnedBhutto that his intelligence service had learned of threats against her life.
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