Search results in Quantum Physics from PIRSA
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Principle of relativity for quantum theory
Marco Zaopo University of Pavia
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An introduction to quantum channels and their capacities
Graeme Smith Institute for Quantum Computing (IQC)
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The effect of initial correlations on the evolution of quantum states
Mark Byrd Southern Illinois University Carbondale
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Holographic Mutual Information is Monogamous
Patrick Hayden Stanford University
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The Ubit Model in Real-Vector-Space Quantum Theory
William Wootters Williams College
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The entropy power inequality for quantum systems
Robert Koenig IBM (United States)
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Why I Am Not a Psi-ontologist
Robert Spekkens Perimeter Institute for Theoretical Physics
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Quantum Reed-Muller Codes and Magic State Distillation in All Prime Dimensions
Dan Browne University College London (UCL) - Department of Physics & Astronomy
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If no information gain implies no disturbance, then any discrete physical theory is classical
(based on http://arxiv.org/abs/1210.0194) It has been suggested that nature could be discrete in the sense that the underlying state space of a physical system has only a finite number of pure states. For example, the Bloch ball of a single qubit could be discretized into small patches and only appear round to us due to experimental limitations. Here, we present a strong physical argument for the quantum theoretical property that every state space (even the smallest possible one, the qubit) has infinitely many pure states. We propose a simple physical postulate which dictates that in fact the only possible discrete theory is classical mechanics. More specifically, we postulate that no information gain implies no disturbance, or read in the contrapositive, that disturbance leads to some form of information gain. In a theory like quantum mechanics where we already know that the converse holds, i.e. information gain does imply disturbance, this can be understood as postulating an equivalence between disturbance and information gain. What is more, we show that non-classical discrete theories are still ruled out even if we relax the postulate to hold only approximately in the sense that no information gain only causes a small amount of disturbance. Finally, our postulate also rules out popular generalizations such as the PR-box that allows non-local correlations beyond the limits of quantum theory. -
Principle of relativity for quantum theory
Marco Zaopo University of Pavia
In a generic quantum experiment we have a given set of devices analyzing some physical property of a system. To each device involved in the experiment we associate a set of random outcomes corresponding to the possible values of the variable analyzed by the device. Devices have apertures that permit physical systems to pass through them. Each aperture is labelled as "input" or "output" depending on whether it is assumed that the aperture lets the system go inside or outside the device. Assuming a particular input/output structure for the devices involved in a generic experiment is equivalent to assume a particular causal structure for the space-time events constituted by the outcomes happening on devices. The joint probability distribution of these outcomes is usually predicted assuming an absolutely defined input/output structure of devices. This means that all observers of the experiment agree on whether an aperture is labelled as "input" or "output". In this talk we show that the mathematical formalism of quantum theory permits to predict the joint probability distribution of outcomes in a generic experiment in such a way that the input/output structure is indeed relative to an observer. This means that two observers of the same experiment can predict the joint probability distribution of outcomes assuming different input/output labels for the apertures. Since input/output structure is the causal structure of the space-time events constituting the outcomes involved in the experiment we conclude that in quantum theory, the causal structure of events may not be regarded as absolute but rather as relative to the observer. We finally point out that properly extending this concept to the cosmological domain could shed light on the problem of dark energy. -
An introduction to quantum channels and their capacities
Graeme Smith Institute for Quantum Computing (IQC)
A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each of these settings there is a capacity that quantifies a channel's fundamental potential for communication. In this introductory talk, I will discuss what we known about the various capacities of a quantum channel, including a discussion of synergies between different channels and related additivity questions. -
Thermodynamics of correlated quantum systems and a generalized exchange fluctuation theorem.
David Jennings Imperial College London
I will discuss the central role of correlations in thermodynamic directionality, how strong correlations can distort the thermodynamic arrow and contrast these distortions in both the classical and quantum regimes. These distortions constitute non-linear entanglement witnesses, and give rise to a rich information-theoretic structure. I shall explain how these results are then cast into the language of fluctuation theorems to derive a generalized exchange fluctuation theorem, and discuss the limitations of such a framework. -
The effect of initial correlations on the evolution of quantum states
Mark Byrd Southern Illinois University Carbondale
Until fairly recently, it was generally assumed that the initial state of a quantum system prepared for information processing was in a product state with its environment. If this is the case,
the evolution is described by a completely positive map. However, if the system and environment are initially correlated, or entangled, such that the so-called quantum discord is non-zero, then the
evolution is described by a map which is not completely positive. Maps that are not completely positive are not as well understood and the implications of having such a map are not completely known. I will discuss a few examples and a theorem (or two) which may help us understand the implications of having maps which are not completely positive. -
Holographic Mutual Information is Monogamous
Patrick Hayden Stanford University
I'll describe a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. Moreover, monogamy property implies that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney, Linden, and Winter; this constitutes significant evidence in favour of its validity. -
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The Ubit Model in Real-Vector-Space Quantum Theory
William Wootters Williams College
It is certainly possible to express ordinary quantum mechanics in the framework of a real vector space: by adopting a suitable restriction on all operators--Stueckelberg’s rule--one can make the real-vector-space theory exactly equivalent to the standard complex theory. But can we achieve a similar effect without invoking such a restriction? In this talk I explore a model within real-vector-space quantum theory in which the role of the complex phase is played by a separate physical system called the ubit (for “universal rebit”). The ubit is a single binary real-vector-space quantum object that is allowed to interact with everything in the world. It also rotates in its two-dimensional state space. In the limit of infinitely fast rotation, one recovers standard quantum theory. When the rotation rate is large but not infinite, one finds small deviations from the standard theory. Here I describe a few such deviations that we have seen numerically and explained analytically. -
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The entropy power inequality for quantum systems
Robert Koenig IBM (United States)
When two independent analog signals, $X$ and $Y$ are added together giving $Z=X+Y$, the entropy of $Z$, $H(Z)$, is not a simple function of the entropies $H(X)$ and $H(Y)$, but rather depends on the details of $X$ and $Y$'s distributions. Nevertheless, the entropy power inequality (EPI), which states that $e^{2H(Z)} \geq e^{2H(X)} + e^{2H(Y)}$, gives a very tight restriction on the entropy of $Z$. This inequality has found many applications in information theory and statistics. The quantum analogue of adding two random variables is the combination of two independent bosonic modes at a beam splitter. The purpose of this talk is to give an outline of the proof of two separate generalizations of the entropy power inequality to the quantum regime. These inequalities provide strong new upper bounds for the classical capacity of quantum additive noise channels, including quantum analogues of the additive white Gaussian noise channels. Our proofs are similar in spirit to standard classical proofs of the EPI, but some new quantities and ideas are needed in the quantum setting. Specifically, we find a new quantum de Bruijin identity relating entropy production under diffusion to a divergence-based quantum Fisher information. Furthermore, this Fisher information exhibits certain convexity properties in the context of beam splitters. This is joint work with Graeme Smith. -
Why I Am Not a Psi-ontologist
Robert Spekkens Perimeter Institute for Theoretical Physics
The distinction between a realist interpretation of quantum theory that is psi-ontic and one that is psi-epistemic is whether or not a difference in the quantum state necessarily implies a difference in the underlying ontic state. Psi-ontologists believe that it does, psi-epistemicists that it does not. This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program. I will review the evidence in favour of the psi-epistemic approach and describe the pre-existing reasons for thinking that if a quantum state represents knowledge about reality then it is not reality as we know it, i.e., it is not the kind of reality that is posited in the standard hidden variable framework. I will argue that the PBR theorem provides additional clues for "what has to give" in the hidden variable framework rather than providing a reason to retreat from the psi-epistemic position. The first assumption of the theorem - that holistic properties may exist for composite systems, but do not arise for unentangled quantum states - is only appealing if one is already predisposed to a psi-ontic view. The more natural assumption of separability (no holistic properties) coupled with the other assumptions of the theorem rules out both psi-ontic and psi-epistemic models and so does not decide between them. The connection between the PBR theorem and other no-go results will be discussed. In particular, I will point out how the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory, regardless of the status of separability (though not in the form posited by PBR). I will also consider the connection of PBR to the failure of local causality by considering an experimental scenario which is in a sense a time-inversion of the PBR scenario. -
Quantum Reed-Muller Codes and Magic State Distillation in All Prime Dimensions
Dan Browne University College London (UCL) - Department of Physics & Astronomy
Joint work with Earl Campbell (FU-Berlin) and Hussain Anwar (UCL) Magic state distillation is a key component of some high-threshold schemes for fault-tolerant quantum computation [1], [2]. Proposed by Bravyi and Kitaev [3] (and implicitly by Knill [4]), and improved by Reichardt [4], Magic State Distillation is a method to broaden the vocabulary of a fault-tolerant computational model, from a limited set of gates (e.g. the Clifford group or a sub-group[2]) to full universality, via the preparation of mixed ancilla qubits which may be prepared without fault tolerant protection. Magic state distillation schemes have a close relation with quantum error correcting codes, since a key step in such protocols [5] is the projection onto a code subspace. Bravyi and Kitaev proposed two protocols; one based upon the 5-qubit code, the second derived from a punctured Reed-Muller code. Reed Muller codes are a very important family of classical linear code. They gained much interest [6] in the early years of quantum error correction theory, since their properties make them well-suited to the formation of quantum codes via the CSS-construction [7]. Punctured Reed-Muller codes (loosely speaking, Reed-Muller codewords with a bit removed) in particular lead to quantum codes with an unusual property, the ability to implement non-Clifford gates transversally [8]. Most work in fault-tolerant quantum computation focuses on qubits, but fault tolerant constructions can be generalised to higher dimensions [9] - particularly readily for prime dimensions. Recently, we presented the first magic state distillation protocols [10] for non-binary systems, providing explicit protocols for the qutrit case (complementing a recent no-go theorem demonstrating bound states for magic state distillation in higher dimensions [11]). In this talk, I will report on more recent work [12], where the properties of punctured Reed-Muller codes are employed to demonstrate Magic State distillation protocols for all prime dimensions. In my talk, I will give a technical account of this result and present numerical investigations of the performance of such a protocol in the qutrit case. Finally, I will discuss the potential for application of these results to fault-tolerant quantum computation. This will be a technical talk, and though some concepts of linear codes and quantum codes will be briefly revised, I will assume that listeners are familiar with quantum error correction theory (e.g. the stabilizer formalism and the CSS construction) for qubits. [1] E. Knill. Fault-tolerant postselected quantum computation: schemes, quant-ph/0402171 [2] R. Raussendorf, J. Harrington and K. Goyal, Topological fault-tolerance in cluster state quantum computation, arXiv:quant-ph/0703143v1 [3] S. Bravyi and A. Kitaev. Universal quantum computation based on a magic states distillation, quant- ph/0403025 [4] B. W. Reichardt, Improved magic states distillation for quantum universality, arXiv:quant-ph/0411036v1 [5] E.T. Campbell and D.E. Browne, On the Structure of Protocols for Magic State Distillation, arXiv:0908.0838
[6] A. Steane, Quantum Reed Muller Codes, arXiv:quant-ph/9608026 [7] Nielsen and Chuang, Quantum Information and Computation, chapter 10 [8] E. Knill, R. Laflamme, and W. Zurek, Threshold accuracy for quantum computation, quant-ph/9610011 [9] D. Gottesman, Fault-Tolerant Quantum Computation with Higher-Dimensional Systems, quant-ph/9802007 [10] H. Anwar, E.T Campbell and D.E. Browne, Qutrit Magic State Distillation, arXiv:1202.2326 [11] V. Veitch, C. Ferrie, J. Emerson, Negative Quasi-Probability Representation is a Necessary Resource for Magic State Distillation, arXiv:1201.1256v3 [12] H. Anwar, E.T Campbell and D.E. Browne, in preparation