arXiv subjects

Lev B. Levitin

Publications and source records attributed to Lev B. Levitin.

8 recordsLinked to original sources

arXiv2009

The fundamental limit on the rate of quantum dynamics: the unified bound is tight

The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a transition from a state to an orthogonal one can be taken as the elementary step of a computational process. Therefore, such a transition can be interpreted as the operation of "flipping a qubit", and the number of orthogonal states visited by the system per unit time can be viewed as the maximum rate of operation. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide, and can be exactly attained by certain initial states if DeltaE=E; however, the problem remained open of what the situation is otherwise. Here we consider the unified bound that takes into account both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE is not equal to E. However, the bound remains tight: for any given values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit value. The relation between the largest energy level, the average energy, and the orthogonalization time is also discussed. These results establish the fundamental quantum limit on the rate of operation of any information-processing system.

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arXiv2007

Thermodynamic cost of reversible computing

Since reversible computing requires preservation of all information throughout the entire computational process, this implies that all errors that appear as a result of the interaction of the information-carrying system with uncontrolled degrees of freedom must be corrected. But this can only be done at the expense of an increase in the entropy of the environment corresponding to the dissipation, in the form of heat, of the ``noisy'' part of the system's energy. This paper gives an expression of that energy in terms of the effective noise temperature, and analyzes the relationship between the energy dissipation rate and the rate of computation. Finally, a generalized Clausius principle based on the concept of effective temperature is presented.

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arXiv2005

Information between quantum systems via POVMs

The concepts of `conditional entropy' and `information' retain their validity for quantum systems, but their properties differ somewhat from those of their classical counterparts; specifically, some equalities and inequalities of classical information theory are in general violated. In this paper the concepts are generalized to include arbitrary indirect measurements (POVMs). Though the generalization is straightforward, it is important to ascertain that the basic relationships between the generalized quantitites remain the same for the POVMs as for direct measurements.

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arXiv2003

Symmetric Autocompensating Quantum Key Distribution

We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarization and time-bin qubits. The primary benefit of the symmetric configuration is that both Alice and Bob may have passive setups (neither Alice nor Bob is required to make active changes for each run of the protocol). We show that both the polarization and the time-bin schemes may be implemented with existing technology. The new schemes are related to previously described schemes by the concept of advanced waves.

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arXiv2003

Maximum speed of quantum gate operation

We consider a quantum gate, driven by a general time-dependent Hamiltonian, that complements the state of a qubit and then adds to it an arbitrary phase shift. It is shown that the minimum operation time of the gate is tau = (h/4E)(1+2 theta/pi), where h is Planck's constant, E is the average over time of the quantum-mechanical average energy, and theta is the phase shift modulo pi.

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arXiv2002

Operation Time of Quantum Gates

We consider a quantum gate that complements the state of a qubit and then adds to it an arbitrary phase shift. It is shown that the minimum operation time of the gate is tau = (h/4E)(1+2 theta/pi), where h is Planck's constant, E is the quantum-mechanical average energy, and theta is the phase shift modulo pi. [We changed the name of a macro file to a more Windows-friendly one, and we clarified the remark "Note that..." after equation (4).]

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arXiv2001

Information and Distinguishability of Ensembles of Identical Quantum States

We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability based on Shannon's 12th theorem, we show that in the case of a single qubit the number of distinguishable states is $W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$, where $(α_1,α_2)$ is the angle interval from which the states are chosen. In the general case of an $N$-dimensional Hilbert space and an area $Ω$ of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is $W(N,n,Ω)=Ω(\frac{2n}{πe})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in Cartesian coordinates.based on Shannon's 12th theorem, we show that in the case of a single qubit the number of distinguishable states is $W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$, where $(α_1,α_2)$ is the angle interval from which the states are chosen. In the general case of an $N$-dimensional Hilbert space and an area $Ω$ of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is $W(N,n,Ω)=Ω(\frac{2n}{πe})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in Cartesian coordinates.

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arXiv1998

The maximum speed of dynamical evolution

We discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time---its maximum speed of dynamical evolution. Previous analyses have given bounds in terms of the standard deviation of the energy of the system; here we give a strict bound that depends only on E-E0, the system's average energy minus its ground state energy. We also discuss bounds on information processing rates implied by our bound on the speed of dynamical evolution. For example, adding one Joule of energy to a given computer can never increase its processing rate by more than about 3x10^33 operations per second.

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