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Quantum Entanglement in the 21St Century

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Quantum Entanglement in the 21St Century Quantum entanglement in the 21 st century John Preskill The Quantum Century: 100 Years of the Bohr Atom 3 October 2013 My well-worn copy, bought in 1966 when I was 13. George Gamow, recalling Bohr’s Theoretical Physics Institute 1928-31: Bohr’s Institute quickly became the world center of quantum physics, and to paraphrase the old Romans, “all roads led to Blegdamsvej 17” … The popularity of the institute was due both to the genius of its director and his kind, one might say fatherly, heart … Almost every country in the world has physicists who proudly say: “I used to work with Bohr.” Thirty Years That Shook Physics , 1966, p. 51. George Gamow, recalling Bohr’s Theoretical Physics Institute 1928-31: Bohr, Fru Bohr, Casimir, and I were returning home from the farewell dinner for Oscar Klein on the occasion of his election as a university professor in his native Sweden. At that late hour the streets of the city were empty. On the way home we passed a bank building with walls of large cement blocks. At the corner of the building the crevices between the courses of the blocks were deep enough to give a toehold to a good alpinist. Casimir, an expert climber, scrambled up almost to the third floor. When Cas came down, Bohr, inexperienced as he was, went up to match the deed. When he was hanging precariously on the second-floor level, and Fru Bohr, Casimir, and I were anxiously watching his progress, two Copenhagen policeman approached from behind with their hands on their gun holsters. One of them looked up and told the other, “Oh, it is only Professor Bohr!” and they went quietly off to hunt for more dangerous bank robbers. Thirty Years That Shook Physics , 1966, p. 57. Werner Heisenberg on Schrödinger’s 1926 visit to Coperhagen: Bohr’s discussions with Schrödinger began at the railway station and continued daily from early morning until late at night. Schrödinger stayed at Bohr’s house so that nothing would interrupt the conversations … After a few days, Schrödinger fell ill, perhaps as a result of his enormous effort; in any case he was forced to keep to his bed with a feverish cold. While Mrs. Bohr nursed him and brought in tea and cake, Niels Bohr kept sitting on the edge of the bed talking at Schrödinger: “But surely you must admit that …” No real understanding could be expected since, at that time, neither side was able to offer a complete and coherent interpretation of quantum mechanics. Physics and Beyond , 1971, p. 73-76. Classical Correlations Classical Correlations Quantum Correlations Aren’t boxes like soxes? Einstein’s 1935 paper, with Podolsky and Rosen (EPR), launched the theory of quantum entanglement. To Einstein, quantum entanglement was so unsettling as to indicate that something is missing from our current understanding of the quantum description of Nature. “If, without in any way disturbing a system, we can predict with certainty … the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.” “there is … no question of a mechanical disturbance of the system under investigation during the critical last stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system.” Quantum entanglement …. This This This This This …. Page Page Page Page Page Blank Blank Blank Blank Blank Nearly all the information in a typical entangled “quantum book” is encoded in the correlations among the “pages”. You can't access the information if you read the book one page at a time. To describe 300 qubits, we would need more numbers than the number of atoms in the visible universe! We can’t even hope to describe the state of a few hundred qubits in terms of classical bits. Might a computer that operates on qubits rather than bits (a quantum computer ) be able to perform tasks that are beyond the capability of any conceivable classical computer? Peter Shor Problems Quantumly Hard Quantumly Easy Classically Easy Problems Quantumly Hard Quantumly Easy Classically Easy What’s in here? Three Questions About Quantum Computers 1. Why build one? How will we use it, and what will we learn from it? A quantum computer may be able to simulate efficiently any process that occurs in Nature! 2. Can we build one? Are there obstacles that will prevent us from building quantum computers as a matter of principle? Using quantum error correction, we can overcome the damaging effects of noise at a reasonable overhead cost. 3. How will we build one? What kind of quantum hardware is potentially scalable to large systems? Quantum entanglement in the 21 st century Algorithms Error Correction Matter Spacetime arXiv papers with “entanglement” in the title 700 600 500 400 300 200 100 0 2005 2006 2007 2008 2009 2010 2011 2012 2013 quant-ph arXiv papers with “entanglement” in the title 450 400 350 300 250 200 150 100 50 0 2005 2006 2007 2008 2009 2010 2011 2012 2013 cond-mat hep-th gr-qc Classical correlations are polygamous Betty Adam Charlie Quantum correlations are monogamous Betty fully entangled unentangled Adam Charlie Quantum correlations are monogamous Betty fully unentangled entangled Adam Charlie Monogamy is frustrating ! Betty fully entangled unentangled cryptography quantum matter black holes Adam Charlie Information Puzzle: singularity Is a black hole a quantum cloner? Suppose that the collapsing body’s quantum information is encoded in “time slice” the emitted Hawking radiation; the information is thermalized , not destroyed. The green time slice crosses both the collapsing body behind the outgoing horizon and nearly all of the radiation radiation outside the horizon. Thus the same (quantum) information is in two places at the same time. event horizon A quantum cloning machine has operated, which is not allowed by the linearity of quantum mechanics. We’re stuck: either information is time destroyed or cloning occurs. Either (outside way, quantum physics needs horizon) collapsing body revision. “Black hole complementarity” singularity Perhaps the lesson is that, for “time slice” mysterious reasons that should be elucidated by a complete theory of quantum gravity, it is wrong to think of the “outside” and “inside” portions of the time slice as two separate outgoing subsystems of a composite system. radiation H H H ≠in ⊗ out event Rather, the inside and outside are horizon merely complementary descriptions of the same system. Which description is appropriate depends on whether the observer enters the time black hole or stays outside (outside (Susskind, 1993). horizon) collapsing body “No-cloning” lower bound on the information retention time Let’s demand that verifiable cloning singularity does not occur. Then the proper time during which Alice can send her qubits to Bob cannot be larger than O(1) in Planck units: Bob (Alice) r trO r τ proper ≈Sexp( −∆ S / S ) ≤ (1) × Planck and therefore t Or r Alice ∆S ≥ ( Slog S ) (where rS is measured in Planck units ). If Alice’s quantum information were revealed in the Hawking radiation faster than this, then Alice and Bob would be able to verify that Alice’s quantum information is in two places at once, in violation of the no-cloning principle. “Black holes as mirrors” Alice throws k qubits (maximally Bob’s decoder entangled with reference ER B' N system N) into an “old” black hole. As radiation R escapes, black reference the correlation of N with B′ hole system decays. Eventually, N is nearly uncorrelated with B′ and nearly V B maximally entangled with a subsystem of ER --- at that radiation black Alice’s stage, Bob can decode Alice’s hole qubits quantum message with high fidelity (Hayden-Preskill, 2007). maximal entanglement time N k dVBNBBNB′ V ′ 2 − c () ρ( )−⊗ ρ ρ max ≤=k+ c = 2 ∫Haar 1 R 2 Bob can decode with high fidelity after receiving only k+c qubits of Hawking radiation, where c is a constant, if the mixing unitary VB is Haar random, or even if it is a typical unitary realized by a small quantum circuit (depth ~log rs). Black hole complementarity challenged Three reasonable beliefs, not all true! [Almheri, Marolf, Polchinski, Sully (AMPS) 2012 ]: (1) The black hole “scrambles” information, but does not destroy it. (2) An observer who falls through the black hole horizon sees nothing unusual (at least for a while). (3) An observer who stays outside the black hole sees nothing unusual. Conservative resolution: A “firewall” at the horizon. Complementarity Challenged singularity (1) For an old black hole, recently emitted radiation (B) is highly entangled with radiation Robert emitted earlier (R) by the time it R reaches Robert. (2) If freely falling observer sees vacuum at the horizon, then the outgoing recently emitted radiation (B) is radiation highly entangled with modes behind the horizon (A). B A (3) If B is entangled with R by the time it reaches Robert, it was already entangled with R at the time time of emission from the black (outside hole. Adam horizon) Betty Monogamy of entanglement violated! event horizon What’s inside a black hole? black hole Bob Alice A. An unlimited amount of stuff. singularity forward light cone “There is all that stuff that fell in and it crashed into the singularity and that’s it. Bye-bye.” – Bill Unruh But … -- Why S = Area / 4? time -- What about AdS/CFT duality? collapsing matter B. Nothing at all. singularity “It is time to constrain and construct the dynamics of firewalls.” – Raphael Bousso time But … -- “Curtains for the equivalence principle?” (Braunstein, 2009) collapsing matter C.
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