**(July 27, 2010)**

*Ludwig-Maximilians-University (LMU)***More Accurate Than Heisenberg Allows? **

**Uncertainty in the Presence of a Quantum Memory**

A ** quantum particle** is hard to grasp, because one cannot determine all its properties precisely at the same time. Measurements of certain parameter pairs such as position and momentum remain inaccurate to a degree given by

**. This is important for the**

*Heisenberg's Uncertainty Principle***, where information is transmitted in the form of quantum states such as the polarization of particles of light. A group of scientists from**

*security of quantum cryptography*

*LMU and the ETH***, including**

*in Zurich***, has now shown that position and momentum can be predicted more precisely than**

*Professor Matthias Christandl***would lead one to expect, if the recipient makes use of a**

*Heisenberg's Uncertainty Principle***that employs ions or atoms. The results show that the magnitude of the uncertainty depends on the degree of correlation ("**

*quantum memory***") between the quantum memory and the quantum particle. "The result not only enhances our understanding of quantum memories, it also provides us with a method for determining the degree of correlation between two quantum particles," says**

*entanglement***. "Moreover, the effect we have observed could yield a means of testing the security of quantum cryptographic systems."**

*Christandl*Unlike classical computers, ** quantum computers** operate not with

**, but with**

*bits***or**

*quantum bits***, quantum mechanical states of particles. The crucial feature of**

*qubits***is that they can exist in different states at once, not just**

*qubits***, but also as a**

*0 or 1***. The ability to exploit**

*superposition of 0 and 1***is what makes quantum computers potentially so powerful. "The goal of our research is to work out how quantum memories, i.e. memory systems for**

*superposition states***, might be utilized in the future and how they affect the transmission of quantum bits," explains**

*qubits***, who left**

*Christandl***in June 2010 to take up a position in the**

*LMU Munich***.**

*Institute of Theoretical Physics at the ETH in Zurich*** Heisenberg's Uncertainty Principle** plays a central role in quantum computing, because it sets a fundamental limit to the accuracy with which a quantum state can be determined. Quantum mechanics also tells us that the measurement of a parameter can itself perturb the state of a particle. If, for example, one were to measure the position of a particle with infinite precision, the particle's momentum would become completely uncertain. Quantum cryptography uses this effect to encrypt data, for instance by entangling two quantum particles in a way that the probability with which the measurement of one particle yields a certain value depends on the state of the other particle. Eavesdropping can thus easily be uncovered, because any measurement will change the state of the particle measured.

The teams at ** LMU and the ETH Zurich** have now shown that the result of a measurement on a quantum particle can be predicted with greater accuracy if information about the particle is available in a quantum memory. Atoms or ions can form the basis for such a quantum memory. The researchers have, for the first time, derived a formula for

**, which takes account of the effect of a quantum memory. In the case of so-called entangled particles, whose states are very highly correlated (i.e. to a degree that is greater than that allowed by the laws of classical physics), the uncertainty can disappear. According to**

*Heisenberg's Principle***, this can be roughly understood as follows "One might say that the disorder or uncertainty in the state of a particle depends on the information stored in the quantum memory. Imagine having a pile of papers on a table. Often these will appear to be completely disordered -- except to the person who put them there in the first place."**

*Christandl*"Our results not only improve our understanding of quantum memories, they also give us a way of measuring entanglement," says ** Christandl**. "The effect could also help us to test the security of quantum cryptographic systems." One can picture the method as a game in which player B transmits a particle to player A. A then performs a measurement on the particle, introducing an uncertainty. A subsequent measurement by B will only yield the value determined by A with an uncertainty given by

**."But if B uses a quantum memory," says**

*Heisenberg's Principle***, "he can determine the correct value and win the game."**

*Christandl***Reference**:

*The uncertainty principle in the presence of quantum memory***Mario Berta, Matthias Christandl, Roger Colbeck, Joseph M. Renes & Renato. Renner.**

*Nature Physics*, published on line 25 July 2010; DOI: 10.1038/nphys1734

Link to Nature Physics abstract

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