Indefinite causal ordering (ICO) refers to quantum channels arranged so that the path through them is a super- position of different possible paths. The ICO is called pure when the path superposition is a pure quantum state. Channel probing, in which probes in prepared quantum states are passed through copies of the channel to estimate one or more channel parameters, is aided by ICO. Specifically, pure ICO is known to increase the quantum Fisher information (QFI) in the processed probe state about the unknown parameter(s). We consider the case complementary to pure ICO in which the path state is maximally mixed for a given indefiniteness. Deriving the QFI under this condition by a new approach, we find that mixed ICO-assisted probing, while not as beneficial as pure ICO probing, still yields greater QFI than does the comparable scheme with definite causal order. The d-dimensional quantum depolarizing channel is used as the channel model for this study. While mixed ICO-assisted probing, like pure ICO-assisted probing, is generally advantageous for probing the depolarizing channel, mixed ICO's relative effectiveness decreases with probe dimension, just as for pure ICO-assisted probing, each being most effective for qubit probes.
Proc. SPIE. 9500, Quantum Information and Computation XIII
KEYWORDS: Energy efficiency, Particles, Energy transfer, Quantum efficiency, Receivers, Feature extraction, Systems modeling, Quantum information, Teleportation, Current controlled current source
Quantum energy teleportation (QET) is a protocol facilitated by a coupled particle pair to enable a sender to transfer energy to a receiver. A variant of the standard QET protocol is proposed in which energy transfer occurs in stages. This allows multiple transfers of energy via the same particle pair, achieving both greater overall efficiency and greater total energy throughput compared to standard QET. Two-stage QET is shown for a particular spin- 1 2 particle pair to simultaneously increase throughput by 36.9% and efficiency by 26.0% over standard QET, while for the same pair three-stage QET increases throughput 38.1% and efficiency 26.7% over standard QET.
Local energy in a component of a multipartite quantum system is the maximum energy that can be extracted by a general (Kraus, operator-sum) local operation on just that component. A component’s local energy is greater or less, or even completely absent, depending on extant correlations with the system’s other components. This is illustrated in different cases of quantum systems of spin-1/2 particles. These cases include a class of two-particle systems with different degrees of coupling anisotropy, three-particle systems, and systems of N particles, generally, with ring and star coupling topologies. Conditions are given in each case for zero local energy. Th3ese conditions establish for each case that, fir systems with a non-degenerate entangled ground state, local energy is absent when the system state is anywhere in a neighborhood of the ground state when the temperature is below critical value in a Gibbs thermal state even systems of many particles.
Energy teleportation with no energy carrier between two physically separated sites was demonstrated
in principle by M. Hotta in 2008. His demonstration used a three-step protocol applied to a Heisenberg
spin particle pair initially in its fully entangled ground state. We apply the Hotta protocol to the
same Heisenberg pair but now suppose the pair is, more generally, in a thermal state, introducing
temperature as an explicit parameter. These thermal states show a degree of quantum correlation
(thermal discord) at all temperatures. We find that at any temperature energy teleportation is
possible with the Hotta protocol, even at temperatures beyond the threshold where the particles’
entanglement vanishes. This shows that entanglement is not fundamentally necessary for energy
teleportation; quantum discord generally can suffice. It is also a new instance in which quantum
dissonance (discord without entanglement) is seen to act as a quantum resource.
Proc. SPIE. 8400, Quantum Information and Computation X
KEYWORDS: Matrices, Physics, Data processing, Mathematics, Quantum physics, Quantum information, Quantum communications, Quantum information processing, Space reconnaissance, Current controlled current source
We consider the problem of identifying the degree of correlation θ in the depolarization rates of an array of qubits,
such as might be found in a holding register in a quantum information processing architecture. We treat this
as a problem in quantum channel identification and use the quantum Fisher information about θ in the channel
output to compare different candidate probe states. We consider channel probes in general pure N-qubit cat
states and find that partial entanglement is always suboptimal; the best cat probe state is either separable or
maximally entangled, and we lay out for any given depolarizing rate p and correlation θ, the (p, θ)-regions for
which separable and maximally entangled probes each yield the most information. In the case of very large
qubit arrays, we find that the quantum Fisher information obtained about θ using any pure cat probe state is
asymptotically independent of the state and identically equal to the information available about a classical coin's
bias from a single coin toss. Finally, we turn our attention to arrays of N qudits (with common dimension D)
that are depolarizing with some correlation θ. We consider both separable and maximally entangled cat probe
states and find and compare their quantum Fisher informations in both the large N and large D regimes.
Quantum mutual information defined in terms of von Neumann entropy captures and quantifies all correlations,
quantum and classical, between the two parts of a bipartite quantum system. Within this framework entanglement
is the most distinguished type of quantum correlation, and a rich body of theory and experiment establishes
that entanglement is a potent and fungible resource for quantum information processing broadly. Bipartite systems
can exhibit quantum correlations beyond entanglement. Such non-classical states are called discordant in
general and strictly discordant (or dissonant) when the quantum state is separable. We show that strict discord
can increase the amount of information available from probing a quantum channel. We focus in this study on
the qubit depolarizing channel, using quantum Fisher information to measure the information available about
the channel depolarizing probability. We consider channel probes prepared, along with an ancilla, in a separable
two-qubit Bell-diagonal state. We prove for Bell-diagonal probes of the qubit depolarizing channel that, in the
absence of entanglement and controlling for marginal purity and degree of classical correlation, any increase in
strict discord between the probe and ancilla yields an accompanying increase in available statistical information
about the channel depolarizing probability.
The classical communication capacities of quantum Pauli channels with memory are known to exhibit
a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task
of Pauli channel memory identification. We treat the complete class of Pauli channels with memory
and determine the maximum quantum Fisher information achievable both with pure separable channel
probe states and with maximally entangled bipartite probe states. A comparison of these Fisher
informations reveals four distinct classes of Pauli channels and shows that only those channels that
exceed a certain parametric threshold exhibit a transition effect. For those Pauli channels that exhibit
this effect, the memory threshold at which it occurs has a simple analytic expression.
The Stern-Gerlach (SG) apparatus for measuring the spin of an uncharged spin-1/2 particle is the archetypal quantum
sensing device. We study this device for the new problem of measuring the spin of a particle that is coupled externally to
another particle. Specifically, we treat two coupled particles in which a single particle is measured by the SG device
while the other is not. We show simulations of how the binding energy associated with the external coupling is
completely converted to potential energy and kinetic energy as the single particle separates spatially within the magnetic
field of the SG device. Additionally we show simulations of how the initial particle acceleration within the SG devices
relates to the coupling, the quantum state of the two-particle system, and the initial spatial dispersion of the particle
within the SG device. The results of our analysis, though obtained specifically for the SG apparatus, may be generic to
other quantum measurement devices with similar external coupling.
The quantum Fisher information is derived for the task of identifying the qudit depolarizing channel
with any dimension. The identification scheme in which a pure state channel input is entangled with an
ancilla system is shown to dominate other schemes for all qudit depolarizing channels of any
dimension and any depolarizing rate. This extends known results for the qubit depolarizing channel.
This dominance, though, is not robust; if the ancilla system itself undergoes any degree of
depolarization, no matter how small, entanglement with the ancilla is no longer necessarily optimal.
The quantum score operator for the qudit depolarizing channel has a special "quasi-classical" form,
readily yielding these various results.
We define quantum state disturbance in terms of Hilbert-Schmidt (HS) distance, finding according to this definition
that measurements and unitary operations drive qubit states along straight lines and circles, respectively, in
HS geometry. We establish conditions for additive disturbance; the straigh-line signature of quantum measurement
is a direct consequence of this additivity. Also, state disturbance defined by HS distance is contrapuntally
related to information gain measured by state discrimination probability. We use these quantifiers of state disturbance
and information gain to elaborate the trade-off between the two. Explicitly identified in this trade-off
between information gain and state disturbance is the mechanism-the measurement strength-that mediates
the trade-off.
A martingale appears in conclusive Bayesian discrimination of two quantum states subjected to a sequence of
optimal weak measurements. This martingale is solely a function of the two system states and their respective
probabilities at the time of each measurement, and it directly determines the evolving probability of discrimination
error. Also, it is constant if and only if the states are pure. For strictly mixed quantum states the martingle
is constant just on average, with the consequence that, with some probability, the realized discrimination error
probability conditioned on prior measurements may be less (better) than the optimal Helstrom error probability.
So for mixed states conditionally superoptimal discrimination is possible. This phenomenon is demonstrated numerically in an example.
We formulate an expression for the accessible information in mirror-symmetric ensembles of real qubit states.
This expression is used to make a detailed study of optimum quantum measurements for extracting the accessible
information in three-state, mirror-symmetric ensembles. Distinct measurement regimes are identified for these
ensembles with optimal measurement strategies involving different numbers of measurement operators, similar to
results found for minimum error discrimination. Our results generalize known results for the accessible information
in two pure states and in the trine ensemble.
A Gaussian statistic, or discriminator, is proposed for conclusively discriminating between two pure quantum states. The discriminator is based on registrations from a limit of an increasing number of weak measurements on a single system. The average error of the discriminator is near that of the optimal conclusive Helstrom discriminator and, in fact, the Gaussian discriminator is the limit point of a class of conclusive discriminators which includes the Helstrom discriminator. The Gaussian discriminator always leaves some post-measurement state (PMS) separation; by contrast, the PMS separation with the Helstrom discriminator is always zero. Simple, closed-form expressions are given for the distribution and error performance of the Gaussian discriminator.