## Profile
Reference frames, super-selection rules and quantum resource theories.
Foundations of Quantum Mechanics ## Outputs
Title | Category | Date | Authors |
On the epistemic view of quantum states University of Calgary | Publication | 2008-01-01 | M. Skotiniotis, A. Roy, B. C. Sanders | Alignment of reference frames and an operational interpretation for the G -asymmetry University of Calgary | Publication | 2012-07-01 | M. Skotiniotis, G. Gour | Quantum Frameness for C P T Symmetry University of Calgary | Publication | 2013-07-01 | M. Skotiniotis, B. Toloui, I. T. Durham, B. C. Sanders | Quantum frameness for CPT inversion symmetry University of Calgary | Publication | 2013-01-01 | M. Skotiniotis, B. Toloui Semnani, I. T. Durham, B. C. Sanders | Alignment of reference frames and an operational interpretation for the G-asymmetry University of Calgary | Publication | 2012-01-01 | M. Skotiniotis, G. Gour | A contextual toy model University of Calgary | Presentation | 2008-08-21 | M. Skotiniotis, G. Gour, A. Roy, B. C. Sanders | Efficient quantum communication under collective noiseWe propose a novel communication protocol for the transmission of quantum information via quantum channels subject to collective noise. Our protocol makes use of decoherence-free subspaces in such a way that an optimal asymptotic rate of transmission is achieved, while at the same time encoding and decoding operations can be implemented efficiently. In particular, for a quantum channel whose collective noise is associated with a discrete group, G, i.e.~with a discrete number, |G|, of possible noise operators, our protocol achieves perfect transmission at a rate of m/(m+r), where r is a finite number of auxiliary systems that depends solely on the channel in question. In the case where the collective noise of the channel is associated with a continuous group, such as a collective phase noise channel, our protocol leads to efficient, approximate transmission of quantum data with arbitrarily high fidelity and optimal transmission rate. The coding and decoding circuit of our protocol requires a number of elementary gates that scale linearly with the number of transmitted qudits, $m$, in contrast to the best known protocols utilizing a decoherence-free subspace.
University of Calgary | Presentation | 2012-02-28 | M. Skotiniotis, B. Krauss, W. Duer | Classical capacity of unspeakable phase information via quantum systemsReference frame alignment, such as synchronization of clocks or alignment of an orthogonal triple of axis, is the communication of unspeakable information and requires physical systems with particular degrees of freedom, such as optical phase or angular momentum. An important property of alignment protocols is the ability to reliably and efficiently transmit such unspeakable information. We derive the optimal rate of transmission of information for the case where two parties wish to align their respective local phase references via the exchange of photons. The rate of transmission depends on the variance of the quantum mechanical state used to encode phase information, and can be achieved by performing collective measurements on N photons.
University of Calgary | Presentation | 2011-07-06 | M. Skotiniotis, G. Gour | Communication of information in the absence of a shared frame of referenceIn a communication protocol the sender, Alice, encodes classical messages by preparing a quantum system in a particular state and sending it to the receiver, Bob, who decodes the message by an appropriate quantum measurement. Implicit in the protocol is the assumption that whatever the physical encoding employed by Alice, whether it is the spin of particle, or the energy levels of an atom, is known to Bob. This assumption amounts to Alice and Bob sharing a common reference frame relative to which the states of physical systems are described. The lack of a shared frame of reference imposes severe restrictions on many communication and computational tasks. We obtain the optimal protocols for two cases: where invariant subspaces are available and where they are not.
University of Calgary | Presentation | 2011-03-09 | M. Skotiniotis, A. Roy, G. Gour, B. C. Sanders | Efficient quantum communication under collective noiseWe introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, $m$. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group $G$, i.e.~with a discrete number, $\lvert G\rvert$, of possible noise operators, perfect transmission at a rate $m/(m+r)$ is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, $r$, solely depends on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, $m$. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements $|G|$. For continuous groups we devise an efficient scheme for approximate transmission, and examine in detail the case of collective phase noise channels described by the group $U(1)$. The same scheme can also be utilized for the storage of quantum information in the presence of collective noise. University of Calgary | Presentation | 2012-06-12 | M. Skotiniotis, W. Duer, B. Krauss | Fully epistemic toy theoryThe Spekkens toy model is an interesting example of how to modify classical physics in order to perform several quantum information processing tasks. Spekkens\' toy model has four axioms concerning toy states, valid operations, measurements, and composition of single toy systems. Motivated by the empirical indistinguishability of epistemic vs. ontic states in the toy universe, we show that relaxing valid operations to mappings of epistemic rather than ontic states preserves the features of the toy model. Similarly we show that relaxing the axiom regarding the composition of single toy systems also preserves the toy model. Relaxing both axioms simultaneously, however, breaks the correspondence of the toy model with quantum theory because the tensor product composition rule is violated, but these two relaxations together produce a group of operations on epistemic states that is isomorphic to the projected extended Clifford Group. University of Calgary | Presentation | 2008-03-11 | M. Skotiniotis, A. Roy, B. C. Sanders | Entanglement-enhanced classical communication without a shared frame of referenceTwo parties, Alice and Bob, share a communication channel but lack a shared reference frame.
Alice's task is to communicate a message to Bob, and she does so by preparing an object in a state
that represents the message, for example as a rotation, and transmitting this object to Bob who
measures the state of the object to reveal the message. Due to the lack of a shared reference frame,
Bob may not be able to perform the appropriate measurement to learn the message. For example
Bob may be lacking the reference angle against which to measure the rotation. Here we tackle the
problem of how two parties, lacking a shared reference frame, could prepare and measure a message
in order to communicate successfully. We deem a prepare-and-measure procedure to be successful
if it minimizes the average error over all received messages.
In our communication protocol the parties circumvent the lack of a shared reference frame by
preparing and sending two objects such that the message is the relative transformation parameter
from the state of the rst object into the state of the second object. Bob performs joint measurements
on the pair of received objects to infer the message from the measurement outcomes. Our aim is
to devise a prepare-and-measure scheme that ensures the highest average success rate for sending
messages as relative transformation parameters between two objects.
We use Schur's lemmas, group representation theory, and quantum estimation theory to derive
optimal measurements given constraints imposed on Alice's preparations. We can nd closed-form
solutions for prepare-and-measure schemes for some constraints and employ numerical methods to
obtain optimal protocols in the more general cases. In particular we discover that, whereas preparing
objects in an entangled state is sucient for success, entanglement is not always necessary. Our
theory lays the groundwork for circumventing a lack of reference frames between parties by sending
messages through the parameter of a relative transformation between two objects. University of Calgary | Presentation | 2010-08-26 | M. Skotiniotis, A. Roy, G. Gour, B. C. Sanders | Operational interpretation of the G-asymmetry for Abelian groupsIn a reference frame alignment protocol the sender, Alice, prepares a quantum system in a state |psi>, that serves as a token of her reference frame, and sends this system to a receiver, Bob, who performs a measurement and learns about the reference frame. We derive the state and measurement that maximize the accessible information in a reference frame alignment protocol. We show that in the limit where a large number of systems are sent, the accessible information per copy equals the Holevo bound. The latter was shown to be equal to the relative entropy of frameness, or G-asymmetry, of the state |psi>, a measure of resourcefulness analogous to the relative entropy of entanglement. We show that for a reference frame alignment protocol, associated with a finite abelian group, Z_N, or the continuous group U(1), associated with the important case of photon number super-selection, the rate of accessible information is quantified by the linearized, regularized G-asymmetry. Our result provides an information theoretic operational interpretation for the G-asymmetry that has been thus far lacking. University of Calgary | Presentation | 2012-02-27 | M. Skotiniotis, G. Gour | Operational Interpretation of the G-asymmetry for Abelian groupsWe determine the quantum states and measurements that optimize the accessible information in a reference frame alignment protocol associated with the groups $U(1)$, corresponding to a phase reference, and $\mathbb{Z}_M$, the cyclic group of $M$ elements. Our result provides
an operational interpretation for the $G$-asymmetry which is information-theoretic and which was thus far lacking. In particular, we show that in the limit of many copies of the bounded-size quantum reference frame, the accessible information approaches the Holevo bound. This implies that
the rate of alignment of reference frames, measured by the (linearized) accessible information per system, is equal to the regularized, linearized $G$-asymmetry. The latter quantity is equal to the variance in the case where $G=U(1)$.
Quite surprisingly, for the case where $G=\mathbb{Z}_{M}$ and $M\geq4$, it is equal to a quantity that is not additive in general, but instead can be superadditive under tensor product of two distinct bounded-size reference frames.
This remarkable phenomenon is purely quantum and has no classical analog. University of Calgary | Presentation | 2012-06-07 | M. Skotiniotis, G. Gour | Operational interpretation of the G-asymmetry for abelian groupsWe determine the quantum states and measurements that optimize the accessible information in a reference frame alignment protocol associated with the groups $U(1)$, corresponding to a phase reference, and $\mathbb{Z}_M$, the cyclic group of $M$ elements. Our result provides an operational interpretation for the $G$-asymmetry which is information-theoretic and which was thus far lacking. In particular, we show that in the limit of many copies of the bounded-size quantum reference frame, the accessible information approaches the Holevo bound. This implies that the rate of alignment of reference frames, measured by the (linearized) accessible information per system, is equal to the regularized, linearized $G$-asymmetry. The latter quantity is equal to the variance in the case where $G=U(1)$. Quite surprisingly, for the case where $G=\mathbb{Z}_{M}$ and $M\geq 4$, it is equal to a quantity that is not additive in general, but instead can be superadditive under tensor product of two distinct bounded-size reference frames. This remarkable phenomenon is purely quantum and has no classical analog. University of Calgary | Presentation | 2012-06-11 | M. Skotiniotis, G. Gour | Quantum frameness for charge-parity-time inversion symmetry University of Calgary | Publication | 2013-01-01 | M. Skotiniotis, B. Toloui Semnani, I. Durham, B. C. Sanders |
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