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Thomas Beth

Publications and source records attributed to Thomas Beth.

At least 37 records · Page 2Linked to original sources
arXiv2002

Complexity of decoupling and time-reversal for n spins with pair-interactions: Arrow of time in quantum control

Well-known Nuclear Magnetic Resonance experiments show that the time evolution according to (truncated) dipole-dipole interactions between n spins can be inverted by simple pulse sequences. Independent of n, the reversed evolution is only two times slower than the original one. Here we consider more general spin-spin couplings with long range. We prove that some are considerably more complex to invert since the number of required time steps and the slow-down of the reversed evolutions are necessarily of the order n. Furthermore, the spins have to be addressed separately. We show for which values of the coupling parameters the phase transition between simple and complex time-reversal schemes occurs.

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arXiv2002

Are there quantum bounds on the recyclability of clock signals in low power computers?

Even if a logical network consists of thermodynamically reversible gate operations, the computation process may have high dissipation rate if the gate implementation is controlled by external clock signals. It is an open question whether the global clocking mechanism necessarily envolves irreversible processes. However, one can show that it is not possible to extract any timing information from a micro-physical clock without disturbing it. Applying recent results of quantum information theory we can show a hardware-independent lower bound on the timing information that is necessarily destroyed if one tries to copy the signal. The bound becomes tighter for low energy signals, i.e., the timing information gets more and more quantum.

quant-ph↗
arXiv2001

Quasi-order of clocks and synchronism and quantum bounds for copying timing information

The statistical state of any (classical or quantum) system with non-trivial time evolution can be interpreted as the pointer of a clock. The quality of such a clock is given by the statistical distinguishability of its states at different times. If a clock is used as a resource for producing another one the latter can at most have the quality of the resource. We show that this principle, formalized by a quasi-order, implies constraints on many physical processes. Similarly, the degree to which two (quantum or classical) clocks are synchronized can be formalized by a quasi-order of synchronism. Copying timing information is restricted by quantum no-cloning and no-broadcasting theorems since classical clocks can only exist in the limit of infinite energy. We show this quantitatively by comparing the Fisher timing information of two output systems to the input's timing information. For classical signal processing in the quantum regime our results imply that a signal looses its localization in time if it is amplified and distributed to many devices.

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arXiv2001

Simulating Hamiltonians in Quantum Networks: Efficient Schemes and Complexity Bounds

We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by applying sequences of appropriate local control sequences. Efficient schemes for decoupling and time reversal can be constructed from orthogonal arrays. Conditions on time optimal simulation are formulated in terms of spectral majorization of matrices characterizing the coupling parameters. Moreover, we consider a specific system of n harmonic oscillators with bilinear interaction. In this case, decoupling can efficiently be achieved using the combinatorial concept of difference schemes. For this type of interactions we present optimal schemes for inversion.

quant-ph↗
arXiv2001

Universal Simulation of Hamiltonians Using a Finite Set of Control Operations

Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this property and present a sufficient condition in terms of group characters. We give examples of such groups in dimension 2 and 3. Furthermore, we show that it is possible to simulate an arbitrary bipartite interaction by a given one using such groups acting locally on the subsystems.

quant-ph↗
arXiv2001

Quantum algorithm for finding periodicities in the spectrum of a black-box Hamiltonian or unitary transformation

Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure eigenvalues of U\otimes U^\dagger even in this case. Running the algorithm several times allows therefore to estimate the autocorrelation function of the density of eigenstates of U. This can be applied to find periodicities in the energy spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a quantum computer.

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arXiv2001

On Using Quantum Protocols to Detect Traffic Analysis

We consider the problem of detecting whether an attacker measures the amount of traffic sent over a communication channel-possibly without extracting information about the transmitted data. A basic approach for designing a quantum protocol for detecting a perpetual traffic analysis of this kind is described.

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arXiv2001

Quantum control without access to the controlling interaction

In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show under which conditions measurements, state preparations, and unitary implementations on the system can be performed by quantum operations on the controller only. It turns out that a measurement of the observable A and an implementation of the one-parameter group exp(iAr) can be performed by almost the same sequence of control operations. Furthermore measurement procedures for A+B, for (AB+BA), and for i[A,B] can be constructed from measurements of A and B. This shows that the algebraic structure of the set of observables can be explained by the Lie group structure of the unitary evolutions on the joint Hilbert space of the measuring device and the measured system. A spin chain model with nearest neighborhood coupling shows that the border line between controller and system can be shifted consistently.

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arXiv2001

Distinguishing n Hamiltonians on C^n by a single measurement

If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way that the different Hamiltonians result in mutual orthogonal final states. We present a general scheme providing such a sequence.

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arXiv2000

A Complexity Measure for Continuous Time Quantum Algorithms

We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over the chromatic index of the interaction graph. This defines a complexity measure of continuous and discrete quantum algorithms which are in exact one-to-one correspondence. Furthermore we prove a lower bound on the growth of large-scale entanglement depending on the chromatic index.

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arXiv2000

Performances of Block Codes Attaining the Expurgated and Cutoff Rate Lower Bounds on the Error Exponent of Binary Classical-Quantum Channels

A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that families of binary block codes with appropriately rescaled binomial multiplicity enumerators used on binary classical-quantum channels and decoded by the suboptimal decision rule introduced by Holevo attain the expurgated and cutoff rate lower bounds on the error exponent.

quant-ph↗
arXiv2000

Remark on multi-particle observables and entangled states with constant complexity

We show that every density matrix of an n-particle system prepared by a quantum network of constant depth is asymptotically commuting with the mean-field observables. We introduce certain pairs of hypersurfaces in the space of density matrices and give lower bounds for the depth of a network which prepares states lying outside those pairs. The measurement of an observable which is not asymptotically commuting with the mean-field observables requires a network of depth in the order of log n, if one demands the measurement to project the state into the eigenspace of the measured observable.

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arXiv2000

The thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the Second Law

Landauer's principle states that the erasure of one bit of information requires the free energy kT ln 2. We argue that the reliability of the bit erasure process is bounded by the accuracy inherent in the statistical state of the energy source (`the resources') driving the process. We develop a general framework describing the `thermodynamic worth' of the resources with respect to reliable bit erasure or good cooling. This worth turns out to be given by the distinguishability of the resource's state from its equilibrium state in the sense of a statistical inference problem. Accordingly, Kullback-Leibler relative information is a decisive quantity for the `worth' of the resource's state. Due to the asymmetry of relative information, the reliability of the erasure process is bounded rather by the relative information of the equilibrium state wit respect to the actual state than by the relative information of the actual state with respect to the equilibrium state (which is the free energy up to constants).

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arXiv1999

Quantum BCH Codes

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed. Finally, parameters of quantum BCH codes are provided.

quant-ph↗
arXiv1999

Quantum Reed-Solomon Codes

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed. Finally, parameters of quantum BCH codes are provided.

quant-ph↗
arXiv1999

Fragility of a class of highly entangled states of many quantum-bits

We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property of showing {\it quantum} uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with 1/\sqrt{n} for all those states which have been exposed to the environment. Furthermore we consider a Quantum Computer with perfect 1-qubit gates and 2-qubit gates with depolarizing error and show that any state which can be obtained from a separable initial state lies inbetween a family of pairs of certain hypersurfaces parallel to those enclosing the separable ones.

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