Probability in decoherent histories

The decoherent (consistent) histories formalism has been proposed as a means of eliminating measurements as a fundamental concept in quantum mechanics. In this formalism, probabilities can be assigned to any description which satisfies a particular consistency condition. The formalism, however, admits incompatible descriptions which cannot be combined, unlike classical physics. This seems to leave an ambiguity in the choice of the description. I argue that this ambiguity is removed by considering the observer as a physical system.Comment: 17 pages, SPROCL LaTeX macros. To appear in proceedings of ``Foundations of Probability in Physics 2, Vaxjo, Sweden, June 2002.'

The Decoherence of Phase Space Histories

In choosing a family of histories for a system, it is often convenient to choose a succession of locations in phase space, rather than configuration space, for comparison to classical histories. Although there are no good projections onto phase space, several approximate projections have been used in the past; three of these are examined in this paper. Expressions are derived for the probabilities of histories containing arbitrary numbers of projections onto phase space, and the conditions for the decoherence of these histories are studied.Comment: 20 pages (RevTex 3.0 macros

Decoherence and quantum trajectories

Decoherence is the process by which quantum systems interact and become correlated with their external environments; quantum trajectories are a powerful technique by which decohering systems can be resolved into stochastic evolutions, conditioned on different possible ``measurements'' of the environment. By calling on recently-developed tools from quantum information theory, we can analyze simplified models of decoherence, explicitly quantifying the flow of information and randomness between the system, the environment, and potential observers.Comment: 14 pages, Springer LNP LaTeX macros, 1 figure in encapsulated postscript format. To appear in proceedings of DICE 200

Computers with closed timelike curves can solve hard problems

A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for the problem of factoring large numbers, and argue that a similar approach can solve NP-complete and PSPACE-complete problems. I discuss the potential impact of quantum effects on this result.Comment: 9 pages LaTeX; submitted to Foundations of Physics Letter

Remotely prepared entanglement: a quantum web page

In quantum teleportation, an unknown quantum state is transmitted from one party to another using only local operations and classical communication, at the cost of shared entanglement. Is it possible similarly, using an $N$ party entangled state, to have the state retrievable by {\it any} of the $N-1$ possible receivers? If the receivers cooperate, and share a suitable state, this can be done reliably. The $N$ party GHZ is one such state; I derive a large class of such states, and show that they are in general not equivalent to the GHZ. I also briefly discuss the problem where the parties do not cooperate, and the relationship to multipartite entanglement quantification. I define a new set of entanglement monotones, the entanglements of preparation.Comment: 13 pages LaTeX. New title. Minor changes and corrections; pointed out monotonicity of entanglement of preparation. To appear in special issue of Algorithmic

Quantum Steganography over Noiseless Channels: Achievability and Bounds

Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for Alice to hide her secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum channel. We calculate achievable rates of steganographic communication over noiseless quantum channels using this encoding. We give definitions of secrecy and reliability for the communication process, and with these assumptions derive upper bounds on the amount of steganographic communication possible, and show that these bounds match the communication rates achieved with our encoding. This gives a steganographic capacity for a noiseless channel emulating a given noisy channel.Comment: 9 pages, 1 figur

Decoherence by Internal Degrees of Freedom

We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom with the internal degrees of freedom. For a simple model of two bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of two harmonically-bound particles moving in an external potential in one dimension, we show that the coupling between the center-of-mass and internal degrees of freedom can be approximated as parametric driving, and that nontrivial coupling depends on the second derivative of the external potential. We find a partial solution to this parametric driving problem. For a simple interference experiment, consisting of two wave packets scattering off of a square well, we perform numerical simulations and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom. We also propose a measure of compositeness which quantifies the extent to which a composite system cannot be approximated as a single, indivisible particle. We numerically calculate this quantity for our square well example system.Comment: 11 pages, 6 figures, minor update adding one referenc

Quantifying non-Markovianity: a quantum resource-theoretic approach

The quantification and characterization of non-Markovian dynamics in quantum systems is an essential endeavor both for the theory of open quantum systems and for a deeper understanding of the effects of non-Markovian noise on quantum technologies. Here, we introduce the robustness of non-Markovianity, an operationally-motivated, optimization-free measure that quantifies the minimum amount of Markovian noise that can be mixed with a non-Markovian evolution before it becomes Markovian. We show that this quantity is a bonafide non-Markovianity measure, since it is faithful, convex, and monotonic under composition with Markovian channels. A two-fold operational interpretation of this measure is provided, with the robustness measure quantifying an advantage in both a state discrimination and a channel discrimination task. Furthermore, we provide a closed-form analytical expression for this measure and show that, quite remarkably, the robustness measure is exactly equal to half the Rivas-Huelga-Plenio (RHP) measure [Phys. Rev. Lett. \textbf{105}, 050403 (2010)]. As a result, we provide a direct operational meaning to the RHP measure while endowing the robustness measure with the physical characterizations of the RHP measure.Comment: 6 + 5 pages, 1 figure, RevTeX 4-1; new results on connection with single-shot information theory and the preorder induced by free super-operation

Suppressing technical noises in weak measurement by entanglement

Postselected weak measurement has aroused broad interest for its distinctive ability to amplify small physical quantities. However, the low postselection efficiency to obtain a large weak value has been a big obstacle to its application in practice, since it may waste resources, and reduce the measurement precision. An improved protocol was proposed in [Phys. Rev. Lett. 113, 030401 (2014)] to make the postselected weak measurement dramatically more efficient by using entanglement. Such a protocol can increase the Fisher information of the measurement to approximately saturate the well-known Heisenberg limit. In this paper, we review the entanglement-assisted protocol of postselected weak measurement in detail, and study its robustness against technical noises. We focus on readout errors. Readout errors can greatly degrade the performance of postselected weak measurement, especially when the readout error probability is comparable to the postselection probability. We show that entanglement can significantly reduce the two main detrimental effects of readout errors: inaccuracy in the measurement result, and the loss of Fisher information. We extend the protocol by introducing a majority vote scheme to postselection to further compensate for readout errors. With a proper threshold, almost no Fisher information will be lost. These results demonstrate the effectiveness of entanglement in protecting postselected weak measurement against readout errors.Comment: 22 pages, 10 figures. This paper extends Phys. Rev. Lett. 113, 030401 (arXiv:1401.5887 [quant-ph]), and studies the effects of technical noises. V2: minor error corrections and close to the published versio

Comment on "Quantum optimization for combinatorial searches"

This is a comment on a recent publication claiming to have found a ``quantum optimization'' algorithm which outperforms known algorithms for minimizing some ``cost function''. Unfortunately, this algorithm is no better than choosing a state at random and checking whether it has low cost.Comment: Final version. Minor changes. Appeared in New Journal of Physic