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### Stability Verification of Quantum non-i.i.d. sources

#### EMV

**Abstract:**
We introduce the problem of stability verification of quantum sources which are non-i.i.d.. These
sources are better described by a Markov chain. This problem is closely related to the problem of
quantum verification first proposed by Pallister et. al. [1], however, it extends the notion of the
original problem. We introduce a family of states that come from these non-i.i.d. sources which we
call a Markov state. We prove in theorem 1 that these states are not well described with tensor
products over a changing source. In theorem 2 we further provide a lower bound on the trace
distance between two Markov states, which is the simplest way to solve the problem of stability
verification of the quantum sources we introduce

### Classicality from Quantum Stochastic Processes

#### EMV

arXiv**Abstract: **
We develop a theory of classicality from quantum systems. This theory stems from
the study of classical and quantum stationary stochastic processes. The stochastic
processes are characterized by polyhedral (classical) and semidefinite representative
(quantum) cones. Based on a previous result \cite{2209.06806v1} we expand the study
of fixed points from quantum channels. We give a semidefinite program that
characterizes a quantum channel separating into a core and a part that decays with
many iterations. In general, the solution is non-separable in the space it is defined.
We present a characterization of channels in terms of their fixed points for the
separable case. A quantum simulation of a polyhedral cone can then be constructed.

### Relativistic time dilation as a quantum mechanism

#### EMV

arXiv**Abstract: **
We propose a mechanism for time dilation using quantum systems. We introduce a
family of operators that are sensitive to the changes of quantum states from
different frames of reference. The change between reference frames is done via
a Galilean transformation, therefore, the source of the dilation in our case
comes from the observable. These observables grow linearly in time and depending
on the reference frame of the state the linear growth changes its slope, therefore
it takes longer to grow to the same point. Such mechanism implies a different
view from the usual understanding of spacetime.

### Quantum Stabilizer Channel for Thermalization

#### EMV

arXiv**Abstract: **
We study the problem of quantum thermalization from a very recent perspective:
via discrete interactions with thermalized systems. We thus extend the previously
introduced scattering thermalization program by studying not only a specific
channel but allowing any possible one. We find a channel that solves a fixed
point condition using the Choi matrix approach that is in general
non-trace-preserving. We find the explicit channel that solves this problem
which yields a condition for trace preservation. From a quantum computing
perspective, the results thus obtained can be interpreted as a condition for
quantum error correction that also reminds of quantum error avoiding.

### Sequential Analysis of a finite number of Coherent states

#### EMV

arXiv**Abstract: **
We investigate an advantage for information processing of ordering a set of
states over making a global quantum processing with a fixed number of copies of
coherent states. Suppose Alice has $N$ copies of one of two quantum states
$\sigma_0$ or $\sigma_1$ and she gives these states to Bob. Using the optimal
sequential test, the SPRT, we ask if processing the states in batches of size $l$
is advantageous to optimally distinguish the two hypotheses. We find that for the
symmetric case $\{|\gamma\rangle,|−\gamma\rangle\}$ there is no advantage of
taking any batch size $l$. We give an expression for the optimal batch size
$l_\text{opt}$ in the assymetric case. We give bounds $l_\text{min}$ and
$l_\text{max}$ for when $P_S\approx1$.

### Online identification of symmetric pure states

#### Gael Sentís, EMV, Ramon Muñoz-Tapia

##### Quantum 6, 658 (2022)

Quantum**Abstract: **We consider online strategies for discriminating between
symmetric pure states with zero error when n copies of the states are
provided. Optimized online strategies involve local, possibly adaptive
measurements on each copy and are optimal at each step, which makes them
robust in front of particle losses or an abrupt termination of the
discrimination process. We first review previous results on binary
minimum and zero error discrimination with local measurements that achieve
the maximum success probability set by optimizing over global measurements,
highlighting their online features. We then extend these results to the
case of zero error identification of three symmetric states with constant
overlap. We provide optimal online schemes that attain global performance
for any n if the state overlaps are positive, and for odd n if overlaps
have a negative value. For arbitrary complex overlaps, we show compelling
evidence that online schemes fail to reach optimal global performance.
The online schemes that we describe only require to store the last
outcome obtained in a classical memory, and adaptiveness of the
measurements reduce to at most two changes, regardless of the value of n.

### Quantum Sequential Hypothesis Testing

#### EMV, Christoph Hirche, Gael Sentís, Michalis Skotiniotis, Marta Carrizo, Ramon Muñoz-Tapia, and John Calsamiglia

##### Phys. Rev. Lett. 126, 180502 (2021)

arXiv PRL**Abstract: **We introduce sequential analysis in quantum information
processing, by focusing on the fundamental task of quantum hypothesis testing.
In particular, our goal is to discriminate between two arbitrary quantum
states with a prescribed error threshold ε when copies of the states can be
required on demand. We obtain ultimate lower bounds on the average number of
copies needed to accomplish the task. We give a block-sampling strategy that
allows us to achieve the lower bound for some classes of states. The bound is
optimal in both the symmetric as well as the asymmetric setting in the sense
that it requires the least mean number of copies out of all other procedures,
including the ones that fix the number of copies ahead of time. For qubit states
we derive explicit expressions for the minimum average number of copies and
show that a sequential strategy based on fixed local measurements outperforms
the best collective measurement on a predetermined number of copies. Whereas
for general states the number of copies increases as log(1/ε), for pure states
sequential strategies require a finite average number of samples even in the
case of perfect discrimination, i.e., ε=0.

### Quantum measurement optimization by decomposition of measurements into extremals

#### EMV, Carlos Pineda, Pablo Barberis-Blostein

##### Scientific Reports volume 10, Article number: 9375 (2020)

Scientific Reports**Abstract: **Using the convex structure of positive operator
value measurements and several quantities used in quantum
metrology, such as quantum Fisher information or the quantum
Van Trees information, we present an efficient numerical method
to find the best strategy allowed by quantum mechanics to
estimate a parameter. This method explores extremal measurements
thus providing a significant advantage over previously used methods.
We exemplify the method for different cost functions in a qubit and
in a harmonic oscillator and find a strong numerical advantage when
the desired target error is sufficiently small.

### Certified answers for ordered quantum discrimination problems

#### EMV and Ramon Muñoz-Tapia

##### Phys. Rev. A 100, 042331 (2019)

ArXiv PRA**Abstract: **We investigate the quantum state discrimination task for
sets of linear independent pure states with an intrinsic ordering. These
structured discrimination problems allow for a scheme that provides a
certified level of error; that is, answers that never deviate from the
true value by more than a specified distance and hence control the desired
quality of the results. We obtain an efficient semidefinite program and also
find a general lower bound valid for any error distance that only requires
the knowledge of an optimal minimum-error scheme. We apply our results to
the cases of quantum change point and quantum state anomaly detection.

### Online optimal exact identification of a quantum change point

#### Gael Sentís, EMV, Ramon Muñoz-Tapia

##### Phys. Rev. A 98, 052305 (2018)

ArXiv PRA**Abstract: **We consider online detection strategies for identifying
a change point in a stream of quantum particles allegedly prepared in
identical states. We show that the identification of the change point
can be done without error via sequential local measurements while
attaining the optimal performance bound set by quantum mechanics. In
this way, we establish the task of exactly identifying a quantum change
point as an instance where local protocols are as powerful as global ones.
The optimal online detection strategy requires only one bit of memory
between subsequent measurements, and it is amenable to experimental
realization with current technology.

### Quantum estimation of unknown parameters

#### EMV, Carlos Pineda, François Leyvraz, and Pablo Barberis-Blostein

##### Phys. Rev. A 95, 012136 (2017)

ArXiv PRA**Abstract: **We discuss the problem of finding the
best measurement strategy for estimating the value of
a quantum system parameter. In general the optimum
quantum measurement, in the sense that it maximizes
the quantum Fisher information and hence allows one
to minimize the estimation error, can only be
determined if the value of the parameter is already
known. A modification of the quantum Van Trees
inequality, which gives a lower bound on the error in
the estimation of a random parameter, is proposed. The
suggested inequality allows us to assert if a
particular quantum measurement, together with an
appropriate estimator, is optimal. An adaptive strategy
to estimate the value of a parameter, based on our
modified inequality, is proposed.